Scientific interests and works are in the field of analytic number theory and mathematical cybernetics:

1. Theory of trigonometric sums and trigonometric integrals:

• the Tarry problem
• the p-adic method
• multiple trigonometric sums
• estimating the Hardy function in the Waring problem
• the Artin problem on local representation of zero by a form
• the Hua Loo Keng problem on the index of convergence of the singular integral in the Tarry problem
• estimating the short Kloostermans sums
• a multidimensional analogue of Waring's problem

2. Theory of the Riemann zeta function:

• the Selberg problem
• zeros of linear combinations of L-series of Dirichlet
• distribution of zeros of the Riemann zeta function on the short intervals of the critical line
• the bound of zeros of the Riemann zeta function and the multidimensional Dirichlet divisor problem
• lower bounds for the maximum modulus of zeta function in small domains of the critical strip and in short intervals of the critical line
• the behavior of the argument of zeta function on the critical line

3. Theory of the Dirichlet characters:

• estimating sums of characters in finite fields
• estimating linear sums of characters in shifted prime numbers
• estimating sums of characters of polynomials with prime argument
• lower bounds for the sums of characters of polynomials
• sums of characters on additive sequences
• distribution of power residues and primitive roots in sparse sequences

4. Theory of finite automata:

• the problem of sharp estimate of the least length of the experiment determining the state of the automaton in the end of the experiment

5. Theory of fast computations:

• the first general method and algorithm for fast multiplication of multiplace numbers – the "divide and conquer" method which had served as the source of a new direction of investigations connected with fast computations
• the complexity of the computation of the functions.

Education and Professional Activities

• 1959 graduated from Faculty of Mechanics and Mathematics of M. V. Lomonosov Moscow State University (MSU) with the speciality "Mathematics".
• Place of employment: Faculty of Mechanics and Mathematics of MSU from February of 1962 till the present time, from 1966 – as co-employment. The main place of employment from 1966: Steklov Institute of Mathematics of Russian Academy of Sciences (MIAN), senior scientific researcher, leading scientific researcher, head of Department of Number Theory from 1983 till the present time.
• Cand. Sci. (Ph.D.) in Mathematics (1962): Ph.D. thesis: "Rational trigonometric sums of a special form and their applications", scientific advisor: professor N. M. Korobov
• Dr. Sci. (Habilitation) thesis (1966): "Method of trigonometric sums and the theorems on the mean value".
• The certificate of professor in Department "Theory of Numbers" (1970), professor of Department "Mathematical Analysis" from 1980 till the present time.
• Member of the specialized Doctor's Councils of Faculty of Mechanics and Mathematics of MSU and of MIAN.
• Member of the Expert Committee of Russian Academy of Sciences (RAS) on the A. A. Markov award and the I. M. Vinogradov award.
• Member of editorial boards of the journals "Izvestiya: Mathematics", "Mathematical Notes", "Mathematica Slovaca".
• Lecturer and head of the research seminars at Faculty of Mechanics and Mathematics of MSU from 1962 till the present time.
• Supervisor of 15 Ph.D. students (Ph.D. degrees in Mathematics obtained from Moscow State University and the Steklov Institute), 7 of them later obtained D.Sci. Habilitation degree.

Prizes and Awards

• The P. L. Chebyshev award of AN USSR (1981), the I. M. Vinogradov award of RAS (2001), Meritorious Science Worker of Russia (1999).