Download or read book The Method of Trigonometrical Sums in the Theory of Numbers written by Ivan M. Vinogradov and published by . This book was released on 1900 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Method of Trigonometrical Sums in the Theory of Numbers written by I. M. Vinogradov and published by Courier Corporation. This book was released on 2013-10-30 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text investigates Waring's problem, approximation by fractional parts of the values of a polynomial, estimates for Weyl sums, distribution of fractional parts of polynomial values, Goldbach's problem, more. 1954 edition.

Download or read book The Method of Trigonometrical Sums in the Theory of Numbers written by Ivan Matveevič Vinogradov (Mathématicien) and published by . This book was released on 1950 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Method of Trigonometrical Sums in the Theory of Numbers by I M Vinogradov Translated from the Russian Revised and Annotated by K F Roth and Anne Davenport written by Ivan Matveevič Vinogradov and published by . This book was released on 1954 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The method of trigonometrical sums on the theory of numbers written by Ivan Matveevich Vinogradov and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Trigonometric Sums in Number Theory and Analysis written by Gennady I. Arkhipov and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the theory of multiple trigonometric sums constructed by the authors. Following a unified approach, the authors obtain estimates for these sums similar to the classical I. M. Vinogradov ́s estimates and use them to solve several problems in analytic number theory. They investigate trigonometric integrals, which are often encountered in physics, mathematical statistics, and analysis, and in addition they present purely arithmetic results concerning the solvability of equations in integers.

Download or read book The Method of Trigonometric Sums in the Theory of Numbers written by I. M. Vinogradoc and published by . This book was released on 1863 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The method of trigonometrical sums in the theory of number written by Ivan M. Vinogradov and published by . This book was released on 1947 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Method of Trigonometrical Sums in the Theory of Number written by Ivan Matveevič Vinogradov and published by . This book was released on 1954 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Method of Trigonometrical Sums in the Theory of Numbers Translated from the Russian Revised and Annotated by K F Roth and Anne Davenport written by Ivan Matveevich VINOGRADOV and published by . This book was released on 1954 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Multiple Trigonometric Sums written by Gennadiĭ Ivanovich Arkhipov and published by American Mathematical Soc.. This book was released on 1982 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the Steklov Institute of Mathematics is a cover-to-cover translation of the Trudy Matematicheskogo Instituta imeni V.A. Steklova of the Russian Academy of Sciences. Each issue ordinarily contains either one book-length article or a collection of articles pertaining to the same topic

Download or read book Trigonometric Sums and Their Applications written by Andrei Raigorodskii and published by Springer Nature. This book was released on 2020-03-11 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents in a unified manner both classic as well as modern research results devoted to trigonometric sums. Such sums play an integral role in the formulation and understanding of a broad spectrum of problems which range over surprisingly many and different research areas. Fundamental and new developments are presented to discern solutions to problems across several scientific disciplines. Graduate students and researchers will find within this book numerous examples and a plethora of results related to trigonometric sums through pure and applied research along with open problems and new directions for future research.

Download or read book Trigonometrical Sums in Number Theory written by Ivan Matveevich Vinogradov and published by . This book was released on 1975 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Basic Analytic Number Theory written by Anatoliĭ Alekseevich Karat͡suba and published by Springer Science & Business Media. This book was released on 1993 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: I. Integer Points.- §1. Statement of the Problem, Auxiliary Remarks, and the Simplest Results.- §2. The Connection Between Problems in the Theory of Integer Points and Trigonometric Sums.- §3. Theorems on Trigonometric Sums.- §4. Integer Points in a Circle and Under a Hyperbola.- Exercises.- II. Entire Functions of Finite Order.- §1. Infinite Products. Weierstrass's Formula.- §2. Entire Functions of Finite Order.- Exercises.- III. The Euler Gamma Function.- §1. Definition and Simplest Properties.- §2. Stirling's Formula.- §3. The Euler Beta Function and Dirichlet's Integral.- Exercises.- IV. The Riemann Zeta Function.- §1. Definition and Simplest Properties.- §2. Simplest Theorems on the Zeros.- §3. Approximation by a Finite Sum.- Exercises.- V. The Connection Between the Sum of the Coefficients of a Dirichlet Series and the Function Defined by this Series.- §1. A General Theorem.- §2. The Prime Number Theorem.- §3. Representation of the Chebyshev Functions as Sums Over the Zeros of the Zeta Function.- Exercises.- VI. The Method of I.M. Vinogradov in the Theory of the Zeta Function.- §1. Theorem on the Mean Value of the Modulus of a Trigonometric Sum.- §2. Estimate of a Zeta Sum.- §3. Estimate for the Zeta Function Close to the Line ? = 1.- §4. A Function-Theoretic Lemma.- §5. A New Boundary for the Zeros of the Zeta Function.- §6. A New Remainder Term in the Prime Number Theorem.- Exercises.- VII. The Density of the Zeros of the Zeta Function and the Problem of the Distribution of Prime Numbers in Short Intervals.- §1. The Simplest Density Theorem.- §2. Prime Numbers in Short Intervals.- Exercises.- VIII. Dirichlet L-Functions.- §1. Characters and their Properties.- §2. Definition of L-Functions and their Simplest Properties.- §3. The Functional Equation.- §4. Non-trivial Zeros; Expansion of the Logarithmic Derivative as a Series in the Zeros.- §5. Simplest Theorems on the Zeros.- Exercises.- IX. Prime Numbers in Arithmetic Progressions.- §1. An Explicit Formula.- §2. Theorems on the Boundary of the Zeros.- §3. The Prime Number Theorem for Arithmetic Progressions.- Exercises.- X. The Goldbach Conjecture.- §1. Auxiliary Statements.- §2. The Circle Method for Goldbach's Problem.- §3. Linear Trigonometric Sums with Prime Numbers.- §4. An Effective Theorem.- Exercises.- XI. Waring's Problem.- §1. The Circle Method for Waring's Problem.- §2. An Estimate for Weyl Sums and the Asymptotic Formula for Waring's Problem.- §3. An Estimate for G(n).- Exercises.- Hints for the Solution of the Exercises.- Table of Prime Numbers

Download or read book International Conference on Analytic Methods in Number Theory and Analysis Moscow 14 19 September 1981 written by and published by American Mathematical Soc.. This book was released on 1986 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection consists of papers delivered at an international conference by the most eminent specialists in the domains of number theory, algebra, and analysis. The papers are devoted to actual problems in these domains of mathematics. In addition, short communications presented by participants in the conference are included.

Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 1988 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: V.1. A-B v.2. C v.3. D-Feynman Measure. v.4. Fibonaccimethod H v.5. Lituus v.6. Lobachevskii Criterion (for Convergence)-Optical Sigman-Algebra. v.7. Orbi t-Rayleigh Equation. v.8. Reaction-Diffusion Equation-Stirling Interpolation Fo rmula. v.9. Stochastic Approximation-Zygmund Class of Functions. v.10. Subject Index-Author Index.

Download or read book Complex Analysis in Number Theory written by Anatoly A. Karatsuba and published by CRC Press. This book was released on 1994-11-22 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the application of complex analysis methods to the theory of prime numbers. In an easy to understand manner, a connection is established between arithmetic problems and those of zero distribution for special functions. Main achievements in this field of mathematics are described. Indicated is a connection between the famous Riemann zeta-function and the structure of the universe, information theory, and quantum mechanics. The theory of Riemann zeta-function and, specifically, distribution of its zeros are presented in a concise and comprehensive way. The full proofs of some modern theorems are given. Significant methods of the analysis are also demonstrated as applied to fundamental problems of number theory.