Contents

Volume 218, 1997

On Professor A. A. Karatsuba’s Works in Mathematics

G. I. Arkhipov and V. N. Chubarikov 1 From the Karatsuba Method for Fast Multiplication of Numbers to Fast Algorithms for Discrete Functions

V. B. Alexeev 15 On the Power of a Singular Set in Binary Additive Problems with Prime Numbers

G. I. Arkhipov, K. Buriev, and V. N. Chubarikov 23 Simultaneous Approximation of Zero by Values of Integral Polynomials

V. I. Bernik and V. N. Borbat 53 On One Method of Estimation of the L_{1}-Norm of an Exponential Sum

S. V. Bochkarev 69 On Interpolation Formulas

S. M. Voronin 72 Third-Degree Diophantine Equations

M. Z. Garaev 94 Limit Theorem with Weight for the Lerch Zeta Function in the Space of Analytic Functions

R. Garunkshtis and A. Laurinchikas 104 On the Complexity of Integration of Rational Fractions

S. B. Gashkov 117 On the Zeros of Linear Combinations of the Analogs of Riemann’s Function

S. A. Gritsenko 129 Orbits of Representation of Numbers by Local Quadratic Forms

V. G. Zhuravlev 146 Difference Equations and the Irrationality Measure of Numbers

V. V. Zudilin 160 On the Exponent of Convergence of Trigonometric Integrals

I. A. Ikromov 175 On the Rationality Problem for Three-Dimensional Algebraic Varieties

V. A. Iskovskikh 186 The Complexity of Circuits of Unit Resistances and Some Properties of Fibonacci Numbers

O. M. Kasim-Zadeh 228 Representation of Numbers by Quadratic Forms

L. A. Kogan 243 Optimisation Problem for the Brunn–Minkowski Inequality

F. M. Malyshev 257 On the Lower Bound of the Number of Variables for the Solvability of the Hilbert–Kamke System in 3-Adic Integers

D. A. Mit’kin 261 The Function ζ̃_{−1}(s) and Formulas of the Second Generation for π(x) and R(x)

J. Moser 282 On the Measure of Algebraic Independence of the Values of Ramanujan Functions

Yu. V. Nesterenko 294 Distribution of Signs in a Sequence of Rectangular Matrices over a Finite Field

V. I. Nechaev 332 Meromorphic Continuation of Dirichlet Series Connected with the Distribution of Numbers Modulo 1

A. I. Pavlov 340 Spherical Convergence of the Fourier Series and Integral of the Indicator of a Two-Dimensional Domain

D. A. Popov 352 Estimates of the Derivatives of Polynomials on Convex Bodies

V. I. Skalyga 372 On the Mean Value of the Ternary Function of Divisors on a Sparse Sequence

H. M. Saliba 384 On the Construction of Probability Measures on Functional Classes

N. T. Temirgaliev 396 Distribution in the Mean in Progressions of Numbers with a Large of Prime Factors

N. M. Timofeev 402 On the Number of Representations of an Odd Integer as a Sum of Three Primes, One of Which Belongs to an Arithmetic Progression

D. I. Tolev 414 On the Algebraic Independence of the Values of Functions Satisfying Systems of Functional Equations

V. G. Chirskii 433 On the Algebraic Independence of the Values of E-Functions

A. B. Shidlovskii 439 On Trigonometric Series with Positive Partial Sums

V. A. Yudin 444