To Prof. Anatolii Alexeevich Karatsuba, on occasion of his 60th birthday
Proc. V.A. Steklov Inst. Math. 218 (1997)
ISBN 5-02-003707-9
This is a collection of papers containing original results in additive number theory, Riemann's Zeta-function and its generalizations, Diophantine approximations, algebraic geometry, oscillating integrals, functions of a real variable, complexity of algorithms and schemes of functional elements.
The book is of interest to researchers and postgraduate students working in analytic number theory and its applications, algebraic geometry, mathematical cybernetics.
Contents (dvi, gzip ps) | |
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G.I. Arkhipov and V.N. Chubarikov "On Professor A.A. Karatsuba's Works in Mathematics" (dvi, gzip ps) | 1–14 |
V.B. Alexeev "From the Karatsuba Method for Fast Multiplication of Numbers to Fast Algorithms for Discrete Functions" (dvi, gzip ps) | 15–22 |
G.I. Arkhipov, K. Buriev, and V.N. Chubarikov "On the Power of a Singular Set in Binary Additive Problems with Prime Numbers" (dvi, gzip ps) | 23–52 |
V.I. Bernik and V.N. Borbat "Simultaneous Approximation of Zero by Values of Integral Polynomials" (dvi, gzip ps) | 53–68 |
S.V. Bochkarev "On One Method of Estimation of the L_{1}-Norm of an Exponential Sum" (dvi, gzip ps) | 69–71 |
S.M. Voronin "On Interpolation Formulas" (dvi, gzip ps) | 72–93 |
M.Z. Garaev "Third-Degree Diophantine Equations" (dvi, gzip ps) | 94–103 |
R. Garunkshtis and A. Laurinchikas "Limit Theorem with Weight for the Lerch Zeta Function in the Space of Analytic Functions" (dvi, gzip ps) | 104–116 |
S.B. Gashkov "On the Complexity of Integration of Rational Fractions" (dvi, gzip ps) | 117–128 |
S.A. Gritsenko "On the Zeros of Linear Combinations of the Analogs of Riemann's Function" (dvi, gzip ps) | 129–145 |
V.G. Zhuravlev "Orbits of Representation of Numbers by Local Quadratic Forms" (dvi, gzip ps) | 146–159 |
V.V. Zudilin "Difference Equations and the Irrationality Measure of Numbers" (dvi, gzip ps) | 160–174 |
I.A. Ikromov "On the Exponent of Convergence of Trigonometric Integrals" (dvi, gzip ps) | 175–185 |
V.A. Iskovskikh "On the Rationality Problem for Three-Dimensional Algebraic Varieties" (dvi, gzip ps) | 186–227 |
O.M. Kasim-Zadeh "The Complexity of Circuits of Unit Resistances and Some Properties of Fibonacci Numbers" (dvi, gzip ps) | 228–242 |
L.A. Kogan "Representation of Numbers by Quadratic Forms" (dvi, gzip ps) | 243–256 |
F.M. Malyshev "Optimisation Problem for the Brunn–Minkowski Inequality" (dvi, gzip ps) | 257–260 |
D.A. Mit'kin "On the Lower Bound of the Number of Variables for the Solvability of the Hilbert–Kamke System in 3-Adic Integers" (dvi, gzip ps) | 261–281 |
J. Moser "The Function _{–1}(s) and Formulas of the Second Generation for π(x) and R(x)" (dvi, gzip ps) | 282–293 |
Yu.V. Nesterenko "On the Measure of Algebraic Independence of the Values of Ramanujan Functions" (dvi, gzip ps) | 294–331 |
V.I. Nechaev "Distribution of Signs in a Sequence of Rectangular Matrices over a Finite Field" (dvi, gzip ps) | 332–339 |
A.I. Pavlov "Meromorphic Continuation of Dirichlet Series Connected with the Distribution of Numbers Modulo 1" (dvi, gzip ps) | 340–351 |
D.A. Popov "Spherical Convergence of the Fourier Series and Integral of the Indicator of a Two-Dimensional Domain" (dvi, gzip ps) | 352–371 |
V.I. Skalyga "Estimates of the Derivatives of Polynomials on Convex Bodies" (dvi, gzip ps) | 372–383 |
H.M. Saliba "On the Mean Value of the Ternary Function of Divisors on a Sparse Sequence" (dvi, gzip ps) | 384–395 |
N.T. Temirgaliev "On the Construction of Probability Measures on Functional Classes" (dvi, gzip ps) | 396–401 |
N.M. Timofeev "Distribution in the Mean in Progressions of Numbers with a Large of Prime Factors" (dvi, gzip ps) | 402–413 |
D.I. Tolev "On the Number of Representations of an Odd Integer as a Sum of Three Primes, One of Which Belongs to an Arithmetic Progression" (dvi, gzip ps) | 414–432 |
V.G. Chirskii "On the Algebraic Independence of the Values of Functions Satisfying Systems of Functional Equations" (dvi, gzip ps) | 433–438 |
A.B. Shidlovskii "On the Algebraic Independence of the Values of E-Functions" (dvi, gzip ps) | 439–443 |
V.A. Yudin "On Trigonometric Series with Positive Partial Sums" (dvi, gzip ps) | 444–447 |
Started on July 2, 1997