This collection consists of papers by participants in the international conference celebrating the 100th anniversary of the birth of I. M. Vinogradov, held in Moscow in September 1991. The papers are devoted to current trends in analytic number theory, function theory, algebraic number theory, algebraic geometry, and combinatorics. The collection begins with a paper by A. A. Karatsuba that describes the life and scientific activity of Vinogradov.

Readership

Graduate students and research mathematicians.

Table of Contents

• A. A. Karatsuba -- I. M. Vinogradov and his method of trigonometric sums; Main dates in the life and activity of I. M. Vinogradov; Chronological index of the works of I. M. Vinogradov
• V. I. Bernik and I. R. Dombrovskiĭ -- Effective estimates of the measure of sets defined by Diophantine conditions
• S. V. Bochkarev -- Estimates of some character sums
• S. M. Voronin -- On an explicit formula for von Mangoldt's \(\Lambda\)-function
• A. I. Galochkin -- On approximation, by algebraic numbers, of the solutions of some equations containing \(E\)-functions
• S. A. Gritsenko -- On a density theorem
• I. Sh. Dzhabbarov -- On estimates of trigonometric integrals
• V. G. Zhuravlev -- Spherical theta-series and Hecke operators
• V. A. Iskovskikh and S. L. Tregub -- Relations in the two-dimensional Cremona group over a nonclosed field
• D. Ismoilov -- Estimates of complete trigonometric sums
• M. I. Israilov and I. A. Allakov -- On the sum of \(k\) th powers of natural numbers
• A. A. Karatsuba -- A new approach to the problem of the zeros of some Dirichlet series
• A. A. Lavrik -- Titchmarsh's problem in the discrete theory of the Riemann zeta-function
• A. F. Lavrik -- The equation of the zeta function and a segment of the Euler product
• A. Laurinchikas -- Limit theorems for Dirichlet \(L\)-functions
• Y. Mozer -- On the multiplicities of the zeros of the Riemann zeta-function
• A. I. Pavlov -- On the number of permutations with a finite set of cycle lengths
• A. A. Polyanskiĭ -- On representation of numbers as the sum of three cubes and a binary quadratic form
• S. Raghavan and J. Sengupta -- On Fourier coefficients of Maass cusp forms in 3-dimensional hyperbolic space
• K. Ramachandra -- Little flowers to I. M. Vinogradov
• Z. Kh. Rakhmonov -- On the distribution of values of Dirichlet characters and their applications
• S. A. Stepanov -- On lower bounds for character sums over finite fields
• M. Sugi -- Lattice points in domains in the Lobachevsky plane
• V. N. Temlyakov -- On error estimates for cubature formulas
• N. M. Timofeev -- Arithmetic functions on the set of shifted primes
• V. G. Chirskiĭ -- Arithmetic properties of values of hypergeometric series
• V. N. Chubarikov -- On Vinogradov's problems in the theory of prime numbers
• A. B. Shidlovskiĭ -- On algebraic independence of the values of \(E\)-functions connected by algebraic equations over the field of rational functions
• K. M. Èminyan -- On the representation of numbers with given properties of the binary expansion by sums of two squares