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Author : KonUL.
Publisher : Unknown
Page : 163 pages
File Size : 49,7 Mb
Release : 1999
Category : Exponential sums
ISBN : OCLC:271786114
Author : Sergei Konyagin,Igor Shparlinski
Publisher : Penguin Group
Page : 182 pages
File Size : 44,8 Mb
Release : 1999-09-02
Category : Computers
ISBN : 0521642639
A treatment of a lively topic from number theory for graduate students and researchers.
Author : N.M Korobov
Publisher : Springer Science & Business Media
Page : 223 pages
File Size : 41,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401580328
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.
Author : Yuri K. Shestopaloff
Publisher : AKVY PRESS
Page : 158 pages
File Size : 41,5 Mb
Release : 2008
Category : Mathematics
ISBN : 9780980966718
Shestopaloff proves new fundamental properties of sums of exponential functions and illustrates application of these properties to different kinds of natural phenomena, particularly applications in biology.
Author : Pascale Charpin,Alexander Pott,Arne Winterhof
Publisher : Walter de Gruyter
Page : 288 pages
File Size : 51,7 Mb
Release : 2013-05-28
Category : Mathematics
ISBN : 9783110283600
This book is based on the invited talks of the "RICAM-Workshop on Finite Fields and Their Applications: Character Sums and Polynomials" held at the Federal Institute for Adult Education (BIfEB) in Strobl, Austria, from September 2-7, 2012. Finite fields play important roles in many application areas such as coding theory, cryptography, Monte Carlo and quasi-Monte Carlo methods, pseudorandom number generation, quantum computing, and wireless communication. In this book we will focus on sequences, character sums, and polynomials over finite fields in view of the above mentioned application areas: Chapters 1 and 2 deal with sequences mainly constructed via characters and analyzed using bounds on character sums. Chapters 3, 5, and 6 deal with polynomials over finite fields. Chapters 4 and 9 consider problems related to coding theory studied via finite geometry and additive combinatorics, respectively. Chapter 7 deals with quasirandom points in view of applications to numerical integration using quasi-Monte Carlo methods and simulation. Chapter 8 studies aspects of iterations of rational functions from which pseudorandom numbers for Monte Carlo methods can be derived. The goal of this book is giving an overview of several recent research directions as well as stimulating research in sequences and polynomials under the unified framework of character theory.
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 50,9 Mb
Release : 2024-06-17
Category : Electronic
ISBN : 9789814466240
Author : Takashi Aoki,Shigeru Kanemitsu,Jianya Liu
Publisher : World Scientific
Page : 267 pages
File Size : 48,5 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814289849
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.
Author : Yuri K. Shestopaloff
Publisher : AKVY PRESS
Page : 229 pages
File Size : 54,6 Mb
Release : 2010
Category : Computers
ISBN : 9780981380025
The book considers properties of polynomial, exponential, logarithmic and power functions. It introduces and proves important relationships between these functions, which enhances the theory and greatly improves the range of theoretical and practical applications, such as the modeling of physical, societal or economical processes. Relationship of the considered functions with the physical reality is another primarily subject of this book. Lots of illustrations and examples based on physical, biological, societal phenomena constitute a substantial part of the book, that facilitates the understanding of introduced modeling concepts and methods. The book is an excellent supplementary material for mathematical and physical courses for undergraduate and graduate studies; a valuable resource for mathematicians working in areas of algebra and analysis. Engineers, researchers, analysts, who use these functions in modeling of different processes and phenomena, will greatly benefit from this book.
Author : Solomon W. Golomb,Matthew G. Parker,Alexander Pott,Arne Winterhof
Publisher : Springer
Page : 421 pages
File Size : 54,6 Mb
Release : 2008-09-15
Category : Computers
ISBN : 9783540859123
This book constitutes the refereed proceedings of the 5th International Conference on Sequences and Their Applications, SETA 2008, held in Lexington, KY, USA in September 2008. The 32 revised full papers presented were carefully reviewed and selected. The papers are organized in topical sections on probabilistic methods and randomness properties of sequences; correlation; combinatorial and algebraic foundations; security aspects of sequences; algorithms; correlation of sequences over rings; nonlinear functions over finite fields.
Author : Gary L. Mullen,Henning Stichtenoth,Horacio Tapia-Recillas
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642594359
The Sixth International Conference on Finite Fields and Applications, Fq6, held in the city of Oaxaca, Mexico, from May 21-25, 2001, continued a series of biennial international conferences on finite fields. This volume documents the steadily increasing interest in this topic. Finite fields are an important tool in discrete mathematics and its applications cover algebraic geometry, coding theory, cryptology, design theory, finite geometries, and scientific computation, among others. An important feature is the interplay between theory and applications which has led to many new perspectives in research on finite fields and other areas. This interplay has been emphasized in this series of conferences and certainly was reflected in Fq6. This volume offers up-to-date original research papers by leading experts in the area.
Author : Claude Carlet,Alexander Pott
Publisher : Springer
Page : 465 pages
File Size : 51,7 Mb
Release : 2010-09-07
Category : Computers
ISBN : 9783642158742
This book constitutes the proceedings of the 6th International Conference on Sequences and Their Applications held in Paris, France, in September 2010.
Author : Joachim von zur Gathen,José Luis Imana
Publisher : Springer Science & Business Media
Page : 214 pages
File Size : 54,5 Mb
Release : 2008-06-25
Category : Computers
ISBN : 9783540694984
This book constitutes the refereed proceedings of the Second International Workshop on the Arithmetic of Finite Fields, WAIFI 2008, held in Siena, Italy, in July 2008. The 16 revised full papers presented were carefully reviewed and selected from 34 submissions. The papers are organized in topical sections on structures in finite fields, efficient finite field arithmetic, efficient implementation and architectures, classification and construction of mappings over finite fields, and codes and cryptography.
Author : Michel Lavrauw
Publisher : American Mathematical Soc.
Page : 216 pages
File Size : 42,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821852989
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.
Author : Bruce Berndt,M.A. Bennett,N. Boston,H.G. Diamond,A.J. Hildebrand,W. Philipp
Publisher : CRC Press
Page : 368 pages
File Size : 41,9 Mb
Release : 2002-11-20
Category : Mathematics
ISBN : 9781000065282
This volume, based on fourteen papers from the Millennial Conference on Number Theory, represents surveys of topics in number theory and provides an outlook into the future of number theory research. It serves as an inspiration to graduate students and as a reference for research mathematicians.
Author : Igor Shparlinski
Publisher : Birkhäuser
Page : 181 pages
File Size : 54,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034886642
The book introduces new techniques which imply rigorous lower bounds on the complexity of some number theoretic and cryptographic problems. These methods and techniques are based on bounds of character sums and numbers of solutions of some polynomial equations over finite fields and residue rings. It also contains a number of open problems and proposals for further research. We obtain several lower bounds, exponential in terms of logp, on the de grees and orders of • polynomials; • algebraic functions; • Boolean functions; • linear recurring sequences; coinciding with values of the discrete logarithm modulo a prime p at suf ficiently many points (the number of points can be as small as pI/He). These functions are considered over the residue ring modulo p and over the residue ring modulo an arbitrary divisor d of p - 1. The case of d = 2 is of special interest since it corresponds to the representation of the right most bit of the discrete logarithm and defines whether the argument is a quadratic residue. We also obtain non-trivial upper bounds on the de gree, sensitivity and Fourier coefficients of Boolean functions on bits of x deciding whether x is a quadratic residue. These results are used to obtain lower bounds on the parallel arithmetic and Boolean complexity of computing the discrete logarithm. For example, we prove that any unbounded fan-in Boolean circuit. of sublogarithmic depth computing the discrete logarithm modulo p must be of superpolynomial size.
