Exponential Sums and their Applications

Exponential Sums and their Applications
Title Exponential Sums and their Applications PDF eBook
Author N.M Korobov
Publisher Springer Science & Business Media
Pages 223
Release 2013-06-29
Genre Mathematics
ISBN 9401580324

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The method of exponential sums is a general method enabling the solution of a wide range of problems in the theory of numbers and its applications. This volume presents an exposition of the fundamentals of the theory with the help of examples which show how exponential sums arise and how they are applied in problems of number theory and its applications. The material is divided into three chapters which embrace the classical results of Gauss, and the methods of Weyl, Mordell and Vinogradov; the traditional applications of exponential sums to the distribution of fractional parts, the estimation of the Riemann zeta function; and the theory of congruences and Diophantine equations. Some new applications of exponential sums are also included. It is assumed that the reader has a knowledge of the fundamentals of mathematical analysis and of elementary number theory.

Sieve Methods, Exponential Sums, and Their Applications in Number Theory

Sieve Methods, Exponential Sums, and Their Applications in Number Theory
Title Sieve Methods, Exponential Sums, and Their Applications in Number Theory PDF eBook
Author G. R. H. Greaves
Publisher Cambridge University Press
Pages 360
Release 1997-01-30
Genre Mathematics
ISBN 0521589576

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State-of-the-art analytic number theory proceedings.

Sequences and Their Applications – SETA 2006

Sequences and Their Applications – SETA 2006
Title Sequences and Their Applications – SETA 2006 PDF eBook
Author Guang Gong
Publisher Springer
Pages 444
Release 2006-09-21
Genre Computers
ISBN 3540445242

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This book constitutes the refereed proceedings of the 4th International Conference on Sequences and Their Applications, SETA 2006. The book presents 32 revised full papers together with 4 invited lectures. The papers are organized in topical sections on linear complexity of sequences, correlation of sequences, stream ciphers and transforms, topics in complexities of sequences, multi-sequence synthesis, sequences and combinatorics, FCSR sequences, aperiodic correlation and applications, and boolean functions, and more.

Theory and Applications of Finite Fields

Theory and Applications of Finite Fields
Title Theory and Applications of Finite Fields PDF eBook
Author Michel Lavrauw
Publisher American Mathematical Soc.
Pages 216
Release 2012
Genre Mathematics
ISBN 0821852981

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This volume contains the proceedings of the 10th International Congress on Finite Fields and their Applications (Fq 10), held July 11-15, 2011, in Ghent, Belgium. Research on finite fields and their practical applications continues to flourish. This volume's topics, which include finite geometry, finite semifields, bent functions, polynomial theory, designs, and function fields, show the variety of research in this area and prove the tremendous importance of finite field theory.

Sequences, Discrepancies and Applications

Sequences, Discrepancies and Applications
Title Sequences, Discrepancies and Applications PDF eBook
Author Michael Drmota
Publisher Springer
Pages 517
Release 2006-11-14
Genre Mathematics
ISBN 354068333X

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The main purpose of this book is to give an overview of the developments during the last 20 years in the theory of uniformly distributed sequences. The authors focus on various aspects such as special sequences, metric theory, geometric concepts of discrepancy, irregularities of distribution, continuous uniform distribution and uniform distribution in discrete spaces. Specific applications are presented in detail: numerical integration, spherical designs, random number generation and mathematical finance. Furthermore over 1000 references are collected and discussed. While written in the style of a research monograph, the book is readable with basic knowledge in analysis, number theory and measure theory.

Geometric Aspects of Functional Analysis

Geometric Aspects of Functional Analysis
Title Geometric Aspects of Functional Analysis PDF eBook
Author Vitali D. Milman
Publisher Springer
Pages 330
Release 2007-04-27
Genre Mathematics
ISBN 3540720537

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This collection of original papers related to the Israeli GAFA seminar (on Geometric Aspects of Functional Analysis) during the years 2004-2005 reflects the general trends of the theory and are a source of inspiration for research. Most of the papers deal with different aspects of the Asymptotic Geometric Analysis, ranging from classical topics in the geometry of convex bodies to the study of sections or projections of convex bodies.

Number Theory: Dreaming In Dreams - Proceedings Of The 5th China-japan Seminar

Number Theory: Dreaming In Dreams - Proceedings Of The 5th China-japan Seminar
Title Number Theory: Dreaming In Dreams - Proceedings Of The 5th China-japan Seminar PDF eBook
Author Shigeru Kanemitsu
Publisher World Scientific
Pages 267
Release 2009-11-26
Genre Mathematics
ISBN 9814466247

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This volume aims at collecting survey papers which give broad and enlightening perspectives of various aspects of number theory.Kitaoka's paper is a continuation of his earlier paper published in the last proceedings and pushes the research forward. Browning's paper introduces a new direction of research on analytic number theory — quantitative theory of some surfaces and Bruedern et al's paper details state-of-the-art affairs of additive number theory. There are two papers on modular forms — Kohnen's paper describes generalized modular forms (GMF) which has some applications in conformal field theory, while Liu's paper is very useful for readers who want to have a quick introduction to Maass forms and some analytic-number-theoretic problems related to them. Matsumoto et al's paper gives a very thorough survey on functional relations of root system zeta-functions, Hoshi-Miyake's paper is a continuation of Miyake's long and fruitful research on generic polynomials and gives rise to related Diophantine problems, and Jia's paper surveys some dynamical aspects of a special arithmetic function connected with the distribution of prime numbers. There are two papers of collections of problems by Shparlinski on exponential and character sums and Schinzel on polynomials which will serve as an aid for finding suitable research problems. Yamamura's paper is a complete bibliography on determinant expressions for a certain class number and will be useful to researchers.Thus the book gives a good-balance of classical and modern aspects in number theory and will be useful to researchers including enthusiastic graduate students.