List of Research Works - Karatsuba Anatolii Alexeevich

Russian page

2011–2000 1999–1990 1989–1980 1979–1970 1969–1960

2011
Karatsuba A. A. A Property of the Set of Primes as a Multiplicative Basis of the Natural Numbers // Doklady Mathematics, v. 84, no. 1, p. 1–4 (2011).
Anatolii A. Karatsuba, A property of the set of prime numbers // Russian Mathematical Surveys, v. 66, no.. 2, p. 209–220 (2011).
2010
Karatsuba A. A. New estimates of short Kloosterman sums // Math. Notes, vol. 88, nos. 3-4, pp. 347–359 (2010).
Anatolii A. Karatsuba, Ekatherina A. Karatsuba. Physical mathematics in number theory // Functional Analysis and Other Mathematics, v. 3, N 1, 13 pp. (2010).
Anatolii A. Karatsuba, Ekatherina A. Karatsuba. On Application of the Functional Equation of the Jacobi Theta Function to Approximation of Atomic Inversion in the Jaynes-Cummings Model // Pacific Journal of Applied Mathematics, v. 2, N 3, 41–63 (2010).
2009
Anatolii A. Karatsuba, Ekatherina A. Karatsuba. Resummation formula for collapse and revival in the Jaynes-Cummings model // J. Phys. A: Math. Theor., 42, 195304, 16 pp. (2009).
Karatsuba A. A., Karatsuba E. A. Application of ATS in a quantum-optical model // Analysis and Mathematical Physics: Trends in Mathematics, Birkhäuser Verlag, Basel, 211–232 (2009).
Karatsuba A. A. Euler and Number theory // Proc. Steklov Inst. Math., 264, 74–86 (2009).
Karatsuba A. A., Karatsuba E. A. The "problem of remainders" in theoretical physics: "physical zeta" function // Proceedings of the 5th MATHEMATICAL PHYSICS MEETING: Summer School and Conference on Modern Mathematical Physics. Ed. by B. Dragovich and Z. Rakic. Institute of Physics, Belgrade, Serbia, pp. 197–210 (2009).
2008
Karatsuba A. A. Nonlinear sums of characters over primes // Doklady Mathematics, 78:1, 508–509 (2008).
Karatsuba A. A. Euler and number theory (Russian) // Leonard Euler and contemporary mathematics, Sovrem. Probl. Mat., 11, 19–37 (2008).
Karatsuba A. A. Arithmetic problems in the theory of Dirichlet characters (Russian, English) // Russ. Math. Surv., 63:4, 641–690 (2008); translation from Usp. Mat. Nauk, 63:4, 43–92 (2008).
2007
Garaev M. Z. and Karatsuba A. A. The representation of residue classes by products of small integers // Proc. Edin. Math. Soc., 50:2, 363–375 (2007).
A. A. Karatsuba, M. A. Korolev, A theorem on the approximation of a trigonometric sum by a shorter one // Izv. RAN. Ser. Mat., 2007, 71:2, 123–150.
A. A. Karatsuba, M. A. Korolev, Approximation of an exponential sum by a shorter one // Dokl. Math., 75:1 (2007).
2006
Karatsuba A. A. The Korobov trigonometric sums (Russian) // Chebyshev's transactions, 7:3(19), 101–109 (2006).
Karatsuba A. A. Zero multiplicity and lower bounds for |ζ(s)| // Functiones et Approximatio, XXXV, 195–209 (2006).
Karatsuba A. A., Korolev M. A. The behavior of the argument of the Riemann zeta function on the critical line (Russian, English) // Russ. Math. Surv., 61:3, (2006); translation from Usp. Mat. Nauk Russ. Math. Surv., 61:3, 3–92 (2006).
Garaev M. Z. and Karatsuba A. A. New estimates of double trigonometric sums with exponential functions // Archiv der Mathematik, 87:1, 33–40 (2006).
2005
Karatsuba A. A. On the number of the changes of sign of the function R₁(x) and of its mean values (Russian) // Chebyshev's transactions, 6:2, 163–183 (2005).
Karatsuba A. A. The behavior of the function R₁(x) and of its mean value // Dokl. Akad. Nauk, 404:4, 439–442 (2005).
Karatsuba A. A. On the Riemann hypothesis (Russian) // Proc. the Conference to the RFBR Decade, Mathematics, Mechanics, Computer Science, 200–209 (2005).
Garaev M. Z. and Karatsuba A. A. On character sums and the exceptional set of a congruence problem // Journal of Number Theory, 114:1, 182–192 (2005).
Karatsuba A. A., Korolev M. A. The argument of the Riemann zeta function // Russ. Math. Surv., 60:3, 433–488 (2005); translation from Usp. Mat. Nauk, 60:3, 41–96 (2005).
2004
Karatsuba A. A. On the approximations of π(x) (Russian) // Chebyshev's transactions, 5:4, 5–20 (2004).
Karatsuba A. A. Principles of analytic number theory, 3-rd ed. (Osnovy analiticheskoj teorii chisel, 3-e izd.) (Russian), Moskva: URSS, 2004, 182 p.
Arkhipov G. I., Chubarikov V. N., Karatsuba A. A. Trigonometric sums in number theory and analysis (English). Berlin–New-York: Walter de Gruyter, 2004, 554 p.
Karatsuba A. A. Lower bounds for the maximum modulus of the Riemann zeta function on short segments of the critical line (Russian, English) // Izv. Math., 68:6, 1157–1163 (2004); translation from Izv. Ross. Akad. Nauk, Ser. Mat., 68:6, 99–104
Karatsuba A. A. On the Riemann Asymptotic Formula for π(x) // Dokl. Math., 69:3, 423 (2004); translation from Dokl. Akad. Nauk, 396:5, 1–2 (2004).
2003
Karatsuba A. A. Omega theorems for zeta sums // Math. Notes, 73:2, 212–217 (2003); translation from Mat. Zametki, 73:2, 228–233 (2003).
Karatsuba A. A. Zeros and Local Extrema of Trigonometric Sums // Problems of Information Transmission, 39:1, 78–91 (2003), translation from Problemy Peredachi Informatsii, 39:1, 87–101 (2003).
2002
Karatsuba A. A. Fractional moments and zeros of ζ(s) on the critical line // Math. Notes, 72:4, 466–472 (2002); translation from Mat. Zametki, 72:4, 502–508 (2002).
Karatsuba A. A. On zeros of trigonometric sums // Dokl. Math., 66:3, 309 (2002); translation from Dokl. Akad. Nauk, 387:1, 1–2 (2002).
2001
Karatsuba A. A. On lower bounds for the Riemann zeta function // Dokl. Math. 63:1, 9 (2001); translation from Dokl. Akad. Nauk, 376:1, 15–16 (2001).
Karatsuba A. A. On fractional parts of rapidly growing functions // Izv. Math., 65:4, 727–748 (2001); translation from Izv. Ross. Akad. Nauk, Ser. Mat., 65:4, 89–110 (2001).
Karatsuba A. A. On a relation between the multidimensional Dirichlet divisor problem and bounds of the zeros of ζ(s) // Math. Notes, 70:3, 432–435 (2001); translation from Mat. Zametki, 70:3, 477–480 (2001).
Karatsuba A. A. Lower bounds for the maximum modulus of ζ(s) in small domains of the critical strip // Math. Notes, 70:5, 724–726 (2001); translation from Mat. Zametki, 70:5, 796–798 (2001).
2000
Karatsuba A. A. Weighted character sums // Izv. Math., 64:2, 249–263 (2000); translation from Izv. Ross. Akad. Nauk, Ser. Mat., 64:2, 29–42 (2000).
Karatsuba A. A. The multidimensional Dirichlet divisor problem and zero free regions for the Riemann zeta function // Functiones et Approximatio, v. XXVIII, p. 131–140 (2000).
Karatsuba A. A. Sums of characters with prime numbers and their applications // Tatra Mountains Math. Publ., v. 20, p. 155–162 (2000).

2010–2000 1999–1990 1989–1980 1979–1970 1969–1960

1999
Karatsuba A. A., Novak B. Arithmetical problems with numbers of special type // Math. Notes, 66:2, 251–253 (1999); translation from Mat. Zametki, 66:2, 315–317 (1999).
Karatsuba A. A. Kloosterman double sums // Math. Notes, 66:5, 565–569 (1999); translation from Mat. Zametki, 66:5, 682–687 (1999).
1998
Karatsuba A. A. Regular sets in residue classes // Math. Notes, 64:2, 190–193 (1998); translation from Mat. Zametki, 64:2, 224–228 (1998).
Karatsuba A. A. An estimate of the L₁-norm of an exponential sum // Math. Notes, 64:3, 401–404 (1998); translation from Mat. Zametki, 64:3, 465–468 (1998).
Karatsuba A. A. Regular sets of the fixed modulo // Acta Math. Inform. Univ. Ostrav., 6:1, 129–134 (1998).
1997
Karatsuba A. A. Additive congruences // Izv. Math., 61:2, 317–329 (1997); translation from Izv. Ross. Akad. Nauk, Ser. Mat., 61:2, 81–94 (1997).
Karatsuba A. A. Analogues of incomplete Kloosterman sums and their applications (Russian)// Tatra Mountains Math. Publ., 11, 89–120 (1997).
1996
Karatsuba A. A. Sums of fractional parts of functions of a special form // Dokl. Math., 54:1, 541 (1996); translation from Dokl. Ross. Akad. Nauk, 349:3, 302 (1996).
Karatsuba A. A. On the function S(t) // Izv. Math., 60:5, 901–931 (1996); translation from Izv. Ross. Akad. Nauk, Ser. Mat., 60:5, 27–56 (1996).
Karatsuba A. A. Density theorem and the behavior of the argument of the Riemann zeta function // Math. Notes, 60:3, 333–334 (1996); translation from Mat. Zametki, 60:3, 448–449 (1996).
1995
Karatsuba A. A. Fractional parts of functions of a special form // Izv. Math., 59:4, 721–740 (1995); translation from Izv. Ross. Akad. Nauk, Ser. Mat., 59:4, 61–80 (1995).
Karatsuba A. A. Analogues of Kloostermans sums // Izv. Math., 59:5, 971–891 (1995); translation from Izv. Ross. Akad. Nauk, Ser. Mat., 59:5, 93–102 (1995).
Karatsuba A. A. On a certain arithmetic function // Russ. Math. Surv., 50:5, 1088–1089 (1995); translation from Usp. Mat. Nauk, 50:5, 247–248 (1995).
Karatsuba A. A. The complexity of computations // Proc. Steklov Inst. Math., 211, 169–183 (1995); translation from Trudy Mat. Inst. Steklova, 211, 186–202 (1995).
Karatsuba A. A. Complex analysis in number theory. Boca Raton, FL: CRC Press, 1995.
1994
Karatsuba A. A. A new approach to the problem of the zeros of some Dirichlet series // Proc. Steklov Inst. Math., 207, 163–177 (1995); translation from Trudy Mat. Inst. Steklova, 207, 180–196 (1994).
Karatsuba A. A. Zeros of the arithmetical Dirichlet series (Russian, English summary) // Math. Slovaca, 44:5, 633–649 (1994).
Voronin S. M., Karatsuba A. A. The Riemann zeta-function (Russian). Moscow: Phys.-Math. Lit., 1994, 376 p.
1993
Karatsuba A. A. On the zeros of arithmetic Dirichlet series without Euler product // Russ. Acad. Sci., Izv. Math., 43:2, 193–203 (1994); translation from Izv. Ross. Akad. Nauk, Ser. Mat., 57:5, 3–14 (1993).
Karatsuba A. A. On the zeros of a class of functions generated by the Hurwitz function // Russ. Math. Surv., 48:5, 175–176 (1993); translation from Usp. Mat. Nauk, 48:5 (293), 175–176 (1993).
Karatsuba A. A. The distribution of inverses in a residue ring modulo a given modulus // Russ. Acad. Sci. Dokl. Math., 48:3, 452–454 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk, 333:2, 138–139 (1993).
Karatsuba A. A. Basic analytic number theory (English), transl. from the Russian by M. B. Nathanson. Berlin: Springer-Verlag, 1993, 222 p.
1992
Karatsuba A. A. On the distribution of real zeros of the function ζ(1/2 + it) // Sov. Math. Dokl., 45:1, 46–47 (1992); translation from Dokl. Akad. Nauk SSSR, 322:2, 217–218 (1992).
Karatsuba A. A. On the number of zeros of the Riemann zeta-function lying in almost all short intervals of the critical line // Russ. Acad. Sci., Izv. Math., 40:2, 353–376 (1993); translation from Izv. Ross. Akad. Nauk, Ser. Mat., 56:2, 372–397 (1992).
Karatsuba A. A., Voronin S. M. The Riemann Zeta-Function. (English, transl. from the Russian by N. Koblitz) Berlin: W. de Gruyter, 1992, 396 p.
Karatsuba A. A. A refinement of theorems on the number of zeros lying on intervals of the critical line of certain Dirichlet series // Russ. Math. Surv., 47:2, 219–220 (1992); translation from Usp. Mat. Nauk, 47:2(284), 193–194 (1992).
Karatsuba A. A. On Zeros of the Davenport–Heilbronn Function // Proc. Amalfi Conf. Analytic Number Theory, p. 271–293 (1992).
1991
Karatsuba A. A. On the zeros of a special type of function connected with Dirichlet series // Math. USSR Izv., 38:3, 471–502 (1992); translation from Izv. Akad. Nauk SSSR, Ser. Mat., 55:3, 483–514 (1991).
Karatsuba A. A. On a density theorem // Proc. Steklov Inst. Math., 200, 205–217 (1993); translation from Trudy Mat. Inst. Steklova, 200, 185–196 (1991).
Karatsuba A. A. Zeros of linear combinations of Z-functions corresponding to Dirichlet series // Sov. Math. Dokl., 43:2, 589–590 (1991); translation from Dokl. Akad. Nauk SSSR, 317:5, 1053–1054 (1991).
Karatsuba A. A. On the zeros of Riemann's Zeta-Function on the critical line // International Symposium in Memory of Hua Loo Keng, 1, 117–162 (1991).
Karatsuba A. A. The distribution of values of Dirichlet characters on additive sequences // Sov. Math. Dokl., 44:1, 145–148 (1992); translation from Dokl. Akad. Nauk SSSR, 319:3, 543–545 (1991).
1990
Karatsuba A. A. Zeros of certain Dirichlet series // Russ. Math. Surv., 45:1, 207–208 (1990); translation from Usp. Mat. Nauk, 45:1 (271), 175–176 (1990).
Karatsuba A. A. On the zeros of the Davenport–Heilbronn function lying on the critical line // Math. USSR Izv., 36:2, 311–324 (1991); translation from Izv. Akad. Nauk SSSR, Ser. Mat., 54:2, 303–315 (1990).
Karatsuba A. A. The distribution of prime numbers // Russ. Math. Surv., 45:5, 99–171 (1990); translation from Usp. Mat. Nauk, 45:5 (275), 81–140 (1990).

2010–2000 1999–1990 1989–1980 1979–1970 1969–1960

1989
Karatsuba A. A. On a diophantine inequality (Russian) // Acta Arithm., LIII, 309–324 (1989).
1988
Karatsuba A. A. Waring's problem in several dimension // Mathem. Forschungs, Oberwolfach, Tagungsbericht, 42, 5 (1988).
1987
Karatsuba A. A. The Hilbert–Kamke problem in analytic number theory // Math. Notes, 41, 155–161 (1987); translation from Mat. Zametki, 41:2, 272–284 (1987).
Arkhipov G. I., Karatsuba A. A. A multidimensional analogue of Waring's problem // Sov. Math. Dokl., 36:1, 75–77 (1987); translation from Dokl. Akad. Nauk SSSR, 295:3, 521–523 (1987).
Karatsuba A. A. The distribution of pairs of quadratic residues and nonresidues of a special form // Math. USSR Izv., 31:2, 307–323 (1988); translation from Izv. Akad. Nauk SSSR, Ser.Mat., 51:5, 994–1009 (1987).
Arkhipov G. I., Karatsuba A. A., Chubarikov V. N. Theory of multiple trigonometric sums (Teoriya kratnykh trigonometricheskikh summ) (Russian) Moskva: Nauka,1987, 368 p.
Karatsuba A. A. Approximation of exponential sums by shorter ones (English) // Proc. Indian. Acad. Sci. (Math. Sci.), 97:1–3, 167–178 (1987).
1986
Karatsuba A. A. On zeros of the Riemann zeta-function on the critical line (English) // Mathem. Forschungs, Oberwolfach, Tagungsbericht, 42, 12 (1986).
1985
Karatsuba A. On the zeros of the Riemann zeta-function on the critical line // Proc. Steklov Inst. Math., 167, 187–200 (1986); translation from Trudy Mat. Inst. Steklova, 167, 167–178 (1985).
Karatsuba A. A. On the zeros of the function ζ(1/2 + it) // Sov. Math. Dokl., 31, 371–373 (1985); translation from Dokl. Akad. Nauk SSSR, 281:5, 1038–1041 (1985).
Karatsuba A. A. On the zeros of the function ζ(s) in the neighborhood of the critical line // Math. USSR Izv., 26, 307–313 (1986); translation from Izv. Akad. Nauk SSSR, Ser. Mat., 49:2, 326–333 (1985).
Karatsuba A. A. On the function G(n) in Waring's problem // Math. USSR Izv., 27, 239–249 (1986); translation from Izv. Akad. Nauk SSSR, Ser. Mat., 49:5, 935–947 (1985).
Karatsuba A. A. On the real zeros of the function ζ(1/2 + it) // Russ. Math. Surv., 40:4, 191–192 (1985); translation from Usp. Mat. Nauk, 40:4(244), 171–172 (1985).
Karatsuba A. A. The Riemann zeta-function and its zeros // Russ. Math. Surv., 40:5, 23–82 (1985); translation from Usp. Mat. Nauk, 40:5(245), 19–70 (1985).
1984
Vinogradov I. M., Karatsuba A. A. The method of trigonometric sums in number theory // Proc. Steklov Inst. Math., 168, 3–30 (1986); translation from Trudy Mat. Inst. Steklova, 168, 4–30 (1984).
Karatsuba A. A. On the zeros of the function ζ(s) on short intervals of the critical line // Math. USSR Izv., 24, 523–537 (1985); translation from Izv. Akad. Nauk SSSR, Ser. Mat., 48:3, 569–584 (1984).
Karatsuba A. A. On zeros of the Riemann zeta-function // Sov. Math. Dokl., 29, 537–540 (1984); translation from Dokl. Akad. Nauk SSSR, 276:3, 535–539 (1984).
Karatsuba A. A. Quadratic residues and nonresidues in sparse sequences // Sov. Math. Dokl., 30, 767–768 (1984); translation from Dokl. Akad. Nauk SSSR, 279:5, 1044–1046 (1984).
Karatsuba A. A. Vinogradov's method of trigonometric sums // Proc. Steklov Inst. Math., 163, 117–123 (1985); translation from Trudy Mat. Inst. Steklova, 163, 97–103 (1984).
Karatsuba A. A. The distribution of zeros of the function ζ(1/2 + it) // Math. USSR Izv., 25, 519–529 (1985); translation from Izv. Akad. Nauk SSSR, Ser. Mat., 48:6, 1214–1224 (1984).
1983
Arkhipov G. I., Karatsuba A. A., Chubarikov V. N. Special cases of the theory of multiple trigonometric sums // Math. USSR Izv., 23, 17–82 (1984); translation from Izv. Akad. Nauk SSSR, Ser. Mat., 47:4, 707–784 (1983).
Arkhipov G. I., Karatsuba A. A., Chubarikov V. N. New uniform estimates for multiple trigonometric sums // Sov. Math. Dokl., 28, 301–303 (1983); translation from Dokl. Akad. Nauk SSSR, 272:1, 11–12 (1983).
Karatsuba A. A. Basic analytic number theory (Russian, English). Berlin: Springer-Verlag, 1993. 222 p. (1993); translation from the book "Karatsuba A. A.: Principles of analytic number theory, 2-nd ed." (Osnovy analiticheskoj teorii chisel, 2-oe izd.) (Russian), Moskva: Nauka, 1983, 236 p.
Karatsuba A. A. On the zeros of the Riemann zeta-function on short intervals of the critical line // Sov. Math. Dokl., 28, 533–535 (1983); translation from Dokl. Akad. Nauk SSSR, 272:6, 1312–1314 (1983).
1982
Arkhipov G. I., Karatsuba A. A. On the representation of zero by a form in the field of p-adic numbers // Sov. Math. Dokl., 25, 1–3 (1982); translation from Dokl. Akad. Nauk SSSR, 262:1, 11–13 (1982).
Arkhipov G. I., Karatsuba A. A. On a problem in the theory of congruences // Russ. Math. Surv., 37:5, 157–158 (1982); translation from Usp. Mat. Nauk, 37:5(227), 161–162 (1982).
1981
Karatsuba A. A. On the distance between adjacent zeros of the Riemann zeta function lying on the critical line // Proc. Steklov Inst. Math., 157, 51–66 (1983); translation from Trudy Mat. Inst. Steklova, 157, 49–63 (1981).
Karatsuba A. A. On a problem with prime numbers // Sov. Math. Dokl., 24, 173–175 (1981); translation from Dokl. Akad. Nauk SSSR, 259:6, 1291–1293 (1981).
Arkhipov G. I., Karatsuba A. A. On local representation of zero by a form // Math. USSR Izv., 19, 231–240 (1982); translation from Izv. Akad. Nauk SSSR, Ser. Mat., 45:5, 948–961 (1981).
1980
Arkhipov G. I., Karatsuba A. A., Chubarikov V. N. On a system of Diophantine equations // Sov. Math. Dokl., 21, 715–717 (1980); translation from Dokl. Akad. Nauk SSSR, 252:2, 275–276 (1980).
Arkhipov G. I., Karatsuba A. A., Chubarikov V. N. Multiple trigonometric sums // Proc. Steklov Inst. Math., 151 (1982), 126 p.; translation from Trudy Mat. Inst. Steklova, 151, 1–128 (1980).
Arkhipov G. I., Karatsuba A. A., Chubarikov V. N. Uniform estimates of multiple trigonometric sums // Sov. Math. Dokl., 21, 904–906 (1980); translation from Dokl. Akad. Nauk SSSR, 252:6, 1289–1291 (1980).
Arkhipov G. I., Karatsuba A. A., Chubarikov V. N. Multiple trigonometric sums and their applications // Math. USSR Izv., 17, 1–54 (1981); translation from Izv. Akad. Nauk SSSR, Ser. Mat., 44:4, 723–781 (1980).

2010–2000 1999–1990 1989–1980 1979–1970 1969–1960

1979
Arkhipov G. I., Karatsuba A. A., Chubarikov V. N. Distribution of fractional parts of polynomials in several variables // Math. Notes, 25, 3–9 (1979); translation from Mat. Zametki, 25:1, 3–14 (1979).
Arkhipov G. I., Karatsuba A. A., Chubarikov V. N. The index of convergence of the singular integral in Tarry's problem // Sov. Math. Dokl., 20, 978–981 (1979); translation from Dokl. Akad. Nauk SSSR, 248:2, 268–272 (1979).
Arkhipov G. I., Karatsuba A. A., Chubarikov V. N. Trigonometric integrals // Math. USSR Izv., 15, 211–239 (1980); translation from Izv. Akad. Nauk SSSR, Ser. Mat., 43:5, 971–1003 (1979).
1978
Karatsuba A. A. The distribution of values of the Legendre symbols of polynomials with prime numbers // Sov. Math. Dokl., 19, 61–63 (1978); translation from Dokl. Akad. Nauk SSSR, 238:3, 524–526 (1978).
Karatsuba A. A. Sums of Legendre symbols of polynomials of second degree over prime numbers // Math. USSR Izv., 12, 299–308 (1978); translation from Izv. Akad. Nauk SSSR, Ser. Mat., 42:2, 315–324 (1978).
Arkhipov G. I., Karatsuba A. A. On I. M. Vinogradov's integral // Sov. Math. Dokl., 19, 389–391 (1978); translation from Dokl. Akad. Nauk SSSR, 239, 764–765 (1978).
Arkhipov G. I., Karatsuba A. A. A new estimate of an integral of I. M. Vinogradov // Math. USSR Izv., 13, 52–62 (1979); translation from Izv. Akad. Nauk SSSR, Ser. Mat., 42:4, 751–762 (1978).
Arkhipov G. I., Karatsuba A. A., Chubarikov V. N. A sharp estimate for the number of solutions of a system of Diophantine equations // Math. USSR Izv., 13, 461–497 (1979); translation from Izv. Akad. Nauk SSSR, Ser. Mat., 42:6, 1187–1226 (1978).
Karatsuba A. A. Asymptotics of an arithmetic sum // Math. Notes, 24, 893–895 (1979); translation from Mat. Zametki, 24:6, 737–740 (1978).
1977
Arkhipov G. I., Karatsuba A. A., Chubarikov V. N. An upper bound for the modulus of a multiple trigonometric sum // Proc. Steklov Inst. Math., 143, 1–31 (1980); translation from Trudy Mat. Inst. Steklova, 143, 3–31 (1977).
1976
Karatsuba A. A. A system of congruences // Math. Notes, 19, 237–239 (1976); translation from Mat. Zametki, 19:3, 389–392 (1976).
Karatsuba A. A. On the distribution of values of nonprincipal characters // Proc. Steklov Inst. Math., 142, 165–174 (1979); translation from Trudy Mat. Inst. Steklov, 142, 156–164 (1976).
1975
Karatsuba A. A. Sums of characters in sequences of shifted prime numbers, with applications // Math. Notes, 17, 91–93 (1975); translation from Mat. Zametki, 17:1, 155–159 (1975).
Karatsuba A. A. Some problems of contemporary analytic number theory // Math. Notes, 17, 195–199 (1975); translation from Mat. Zametki, 17:2, 341–350 (1975).
Karatsuba A. A. On some arithmetic problems with numbers having small prime divisors (Russian) // Acta Arithmetica, 27, 489–492 (1975).
Karatsuba A. A. Trigonometric sums and their applications // Amer. Math. Soc., Translat., II. Ser., 109, 9–11 (1977); translation from Proc. Int. Congr. Math., Vancouver 1974, 1, 365–368 (1975).
Karatsuba A. A. Fundamentos de la teoria analitica de los numeros (Russian, Spanish, Chinese); Moscu: Mir, 1979, 244 p.; translation from the book "Karatsuba A. A. Principles of analytic number theory" (Osnovy analiticheskoj teorii chisel) (Russian), Moskva: Nauka, 1975, 183 p.
Karacuba A. A. Experimente mit Automaten (German) // Elektron. Inform.-verarb. Kybernetik, 11, 611–612 (1975).
Karacuba A. A. Berechnungen und die Kompliziertheit von Beziehungen (German) // Elektron. Inform.-verarb. Kybernetik, 11, 603–606 (1975).
1973
Karatsuba A. A. On some problems of prime number theory connected with I. M. Vinogradov's method // Proc. Steklov Inst. Math., 132, 293–298 (1975); translation from Trudy Mat. Inst. Steklova, 132 (Trudy Mezhdunarod. Konf. Teor. Chisel, Moskva 1971), 257–261 (1973).
Karatsuba A. A. Lower estimates of sums of polynomial characters // Math. Notes, 14, 593–596 (1974); translation from Mat. Zametki, 14:1, 67–72 (1973).
Karatsuba A. A. The mean value of the modulus of a trigonometric sum // Math. USSR Izv., 7, 1199–1223 (1975); translation from Izv. Akad. Nauk SSSR, Ser. Mat., 37:6, 1203–1227 (1973).
1972
Karatsuba A. A. The Dirichlet divisor problem in number fields // Sov. Math. Dokl., 13, 697–698 (1972); translation from Dokl. Akad. Nauk SSSR, 204:3, 540–541 (1972).
Karatsuba A. A. Uniform estimate of the remainder in the problem of Dirichlet divisors // Izv. Akad. Nauk SSSR, Ser. Mat., 36:3, 475–483 (1972).
1971
Karatsuba A. A. Distribution of power residues and nonresidues in additive sequences // Sov. Math. Dokl., 12, 235–236 (1971); translation from Dokl. Akad. Nauk SSSR, 196:4, 759–760 (1971).
Karatsuba A. A. Sums of characters with prime numbers in an arithmetic progression // Math. USSR Izv., 5, 485–501 (1972); translation from Izv. Akad. Nauk SSSR, Ser. Mat., 35:3, 469–484 (1971).
Karatsuba A. A. On a certain arithmetic sum // Sov. Math. Dokl., 12, 1172–1174 (1971); translation from Dokl. Akad. Nauk SSSR, 199:4, 770–772 (1971).
Karatsuba A. A. Estimates for trigonometric sums by Vinogradov's method and some applications // Proc. Steklov Inst. Math., 112, 251–265 (1973); translation from Trudy Mat. Inst. Steklova, 112, 241–255 (1971).
1970
Karatsuba A. A. On sums of characters with primes // Sov. Math. Dokl., 11, 135–137 (1970); translation from Dokl. Akad. Nauk SSSR, 190:3, 517–518 (1970).
Karatsuba A. A. On estimates of sums of characters // Math. USSR Izv., 4, 19–29 (1970); translation from Izv. Akad. Nauk SSSR, Ser. Mat., 34:1, 20–30 (1970).
Karatsuba A. A. Sums of characters with prime numbers // Math. USSR Izv., 4, 303–326 (1970); translation from Izv. Akad. Nauk SSSR, Ser. Mat., 34:2, 299–321 (1970).
Karatsuba A. A. The distribution of products of shifted primes in arithmetical progressions // Sov. Math. Dokl., 11, 707–711 (1970); translation from Dokl. Akad. Nauk SSSR, 192:4, 724–727 (1970).

2010–2000 1999–1990 1989–1980 1979–1970 1969–1960

1969
Karatsuba A. A. On trigonometric sums // Sov. Math. Dokl., 10, 1334–1337 (1969); translation from Dokl. Akad. Nauk SSSR, 189:1, 31–34 (1969).
1968
Karatsuba A. A. About a system of indeterminate equations // Math. Notes, 4, 565–567 (1968); translation from Mat. Zametki, 4:2, 125–128 (1968).
Karatsuba A.A. On an asymptotic formula // Trans. Moscow Math. Soc., 18, 85–90 (1968); translation from Trudy Mosk. Mat. Obshch., 18, 77–82 (1968).
Karatsuba A. A. Character sums and primitive roots in finite fields // Sov. Math. Dokl., 9, 755–757 (1968); translation from Dokl. Akad. Nauk SSSR, 180:6, 1287–1289 (1968).
1967
Karatsuba A. A. Method of trigonometric sums and the mean value theorems (Russian) // Mat. Zametki, 1:1, 99–110 (1967).
Karatsuba A. A. Estimates of complete trigonometric sums (Russian) // Mat. Zametki, 1:2, 199–208 (1967).
1966
Karatsuba A. A. The mean value theorems and complete trigonometric sums (Russian) // Izv. Akad. Nauk SSSR, Ser. Mat., 30:1, 183–206 (1966).
Karatsuba A. A. Method of trigonometric sums and the mean value theorems (Russian) // Habilitation Thesis, MIAN, 1966, 144 p.
Karatsuba A. A. Asymptotic formulas for a class of trigonometric sums // Sov. Math. Dokl., 7, 134–136 (1966); translation from Dokl. Akad. Nauk SSSR, 169:1, 9–11 (1966).
1965
Karatsuba A. A. On systems of congruences // Amer. Math. Soc., Transl., II. Ser., 82, 73–84 (1969); translation from Izv. Akad. Nauk SSSR, Ser. Mat., 29:4, 935–944 (1965).
Karatsuba A. A. On the estimation of the number of solutions of certain equations // Sov. Math. Dokl., 6, 1402–1404 (1966); translation from Dokl. Akad. Nauk SSSR, 165:1, 31–32 (1965).
Karatsuba A. A. Systems of congruences and equations of Waring type // Sov. Math. Dokl., 6, 1439–1441 (1966); translation from Dokl. Akad. Nauk SSSR, 165:2, 274–276 (1965).
1964
Karatsuba A. A. Trigonometric sums of a special form and their applications (Russian) // Izv. Akad. Nauk SSSR, Ser. Mat., 28:1, 237–248 (1964).
Karatsuba A. A. Supplement N 4 to the Hua Loo Keng book "Method of trigonometric sums and their application in number theory" (Russian). Moscow: Mir, 180–187 (1964).
1963
Karatsuba A. A., Korobov N. M. On the mean-value theorem // Sov. Math. Dokl., 4, 350–354 (1963); translation from Dokl. Akad. Nauk SSSR, 149:2, 245–248 (1963).
1962
Karatsuba A., Ofman Yu. Multiplication of multidigit numbers on automata // Soviet Physics-Doklady, 7, 595–596 (1963); translation from Dokl. Akad. Nauk SSSR, 145:2, 293–294, (1962).
Karatsuba A. A. The analog of the Waring problem (Russian) // Vestn. Mosk. Univ., Ser. 1, 1, 38–46 (1962).
Karatsuba A. A. The distribution of the fractional parts of polynomials of a special form (Russian) // Vestn. Mosk. Univ., Ser. 1, 3, 34–38 (1962)
Karatsuba A. A. The Waring problem for the congruence modulo the number which is equal to the prime in power (Russian) // Vestn. Mosk. Univ., Ser. 1, 4, 28–38 (1962).
Karatsuba A. A. Rational trigonometric sums of a special form and their applications. Ph.D. Thesis, MGPI, 1962, 60 p.
1961
Karatsuba A. A. Tarry problem for a system of congruences (Russian) // Math. Sb., 55:2, 209–220 (1961).
Karatsuba A. A. Estimates of trigonometric sums of a special form and their applications // Sov. Math. Dokl., 2, 304–305 (1961); translation from Dokl. Akad. Nauk SSSR, 137:3, 513–514 (1961).
1960
Karatsuba A. A. Solution to a problem in the theory of finite automata (Russian) // Usp. Mat. Nauk, 15:3(93) 157–159 (1960).

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