Download or read book Sieve Methods Exponential Sums and Their Applications in Number Theory written by G. R. H. Greaves and published by Cambridge University Press. This book was released on 1997-01-30 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: State-of-the-art analytic number theory proceedings.
Download or read book Sieve Methods Exponential Sums and Their Applications in Number Theory written by G. R. H. Greaves and published by . This book was released on 1997 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: State-of-the-art analytic number theory proceedings.
Download or read book Sieve Methods Exponential Sums and Their Applications in Number Theory written by George Richard Herbert Greaves and published by . This book was released on 2014-05-14 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: State-of-the-art analytic number theory proceedings.
Download or read book Exponential Sums and their Applications written by N.M Korobov and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Higher Dimensional Sieve Method written by Harold G. Diamond and published by Cambridge University Press. This book was released on 2008-10-16 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nearly a hundred years have passed since Viggo Brun invented his famous sieve, and the use of sieve methods is constantly evolving. As probability and combinatorics have penetrated the fabric of mathematical activity, sieve methods have become more versatile and sophisticated and in recent years have played a part in some of the most spectacular mathematical discoveries. Many arithmetical investigations encounter a combinatorial problem that requires a sieving argument, and this tract offers a modern and reliable guide in such situations. The theory of higher dimensional sieves is thoroughly explored, and examples are provided throughout. A Mathematica® software package for sieve-theoretical calculations is provided on the authors' website. To further benefit readers, the Appendix describes methods for computing sieve functions. These methods are generally applicable to the computation of other functions used in analytic number theory. The appendix also illustrates features of Mathematica® which aid in the computation of such functions.
Download or read book Number Theory written by R.P. Bambah and published by Birkhäuser. This book was released on 2012-12-06 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Indian National Science Academy on the occasion ofthe Golden Jubilee Celebration (Fifty years of India's Independence) decided to publish a number of monographs on the selected fields. The editorial board of INS A invited us to prepare a special monograph in Number Theory. In reponse to this assignment, we invited several eminent Number Theorists to contribute expository/research articles for this monograph on Number Theory. Al though some ofthose invited, due to other preoccupations-could not respond positively to our invitation, we did receive fairly encouraging response from many eminent and creative number theorists throughout the world. These articles are presented herewith in a logical order. We are grateful to all those mathematicians who have sent us their articles. We hope that this monograph will have a significant impact on further development in this subject. R. P. Bambah v. C. Dumir R. J. Hans-Gill A Centennial History of the Prime Number Theorem Tom M. Apostol The Prime Number Theorem Among the thousands of discoveries made by mathematicians over the centuries, some stand out as significant landmarks. One of these is the prime number theorem, which describes the asymptotic distribution of prime numbers. It can be stated in various equivalent forms, two of which are: x (I) K(X) '" -I - as x --+ 00, ogx and Pn '" n log n as n --+ 00. (2) In (1), K(X) denotes the number of primes P ::s x for any x > O.
Download or read book Number Theory written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sieves in Number Theory written by George Greaves and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys the current state of the "small" sieve methods developed by Brun, Selberg and later workers. The book is suitable for university graduates making their first acquaintance with the subject, leading them towards the frontiers of modern research and unsolved problems in the subject area.
Download or read book Analytic Number Theory written by Yoichi Motohashi and published by Cambridge University Press. This book was released on 1997-10-16 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Authoritative, up-to-date review of analytic number theory containing outstanding contributions from leading international figures.
Download or read book Surveys in Number Theory written by Bruce Berndt and published by CRC Press. This book was released on 2002-11-20 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Number Theory written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Number Theory Arithmetic in Shangri La written by Shigeru Kanemitsu and published by World Scientific. This book was released on 2013-02-20 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on the successful 6th China–Japan Seminar on number theory that was held in Shanghai Jiao Tong University in August 2011. It is a compilation of survey papers as well as original works by distinguished researchers in their respective fields. The topics range from traditional analytic number theory — additive problems, divisor problems, Diophantine equations — to elliptic curves and automorphic L-functions. It contains new developments in number theory and the topics complement the existing two volumes from the previous seminars which can be found in the same book series. Contents:On Jacobi Forms with Levels (Hiroki Aoki)Additive Representation in Thin Sequences, VIII: Diophantine Inequalities in Review (Jörg Brüdern, Koichi Kawada and Trevor D Wooley)Annexe to the Gallery: An Addendum to “Additive Representation in Thin Sequences, VIII: Diophantine Inequalities in Review” (Jörg Brüdern, Koichi Kawada and Trevor D Wooley)A Note on the Distribution of Primes in Arithmetic Progressions (Zhen Cui and Boqing Xue)Matrices of Finite Abelian Groups, Finite Fourier Transform and Codes (Shigeru Kanemitsu and Michel Waldschmidt)A Remark on a Result of Eichler (Yoshiyuki Kitaoka)On Weyl Sums over Primes in Short Intervals (Angel V Kumchev)On Congruences for Certain Binomial Coefficients of E Lehmer's Type (Takako Kuzumaki and Jerzy Urbanowicz)Sign Changes of the Coefficients of Automorphic L-Functions (Yuk-Kam Lau, Jianya Liu and Jie Wu)On Fourier Coefficients of Automorphic Forms (Guangshi Lü)The Twists of Hessian Elliptic Curves over Splitting Fields of Cubic Polynomials and the Related Elliptic 3-Folds (Katsuya Miyake)Asymptotic Voronoi's Summation Formulas and Their Duality for SL3(ℤ) (Xiumin Ren and Yangbo Ye)Jerzy Urbanowicz's Work in Pure Mathematics (Andrzej Schinzel)Conjectures Involving Arithmetical Sequences (Zhi-Wei Sun) Readership: Graduate students and researchers in number theory. Keywords:Diophantine Equation;Hessian Elliptic Curves;Automorphic L-functions;Jacobi Forms;Weyl Sums;Fourier Coefficients;Result of Eichler;Distribution of Primes in Arithmetic Progression
Download or read book Number Theory written by Takashi Aoki and published by World Scientific. This book was released on 2010 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 OCo 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 OCo 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, HoshiOCoMiyake''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. Sample Chapter(s). Chapter 1: Resent Progress on the Quantitative Arithmetic of Del Pezzo Surfaces (329 KB). Contents: Recent Progress on the Quantitative Arithmetic of Del Pezzo Surfaces (T D Browning); Additive Representation in Thin Sequences, VIII: Diophantine Inequalities in Review (J Brdern et al.); Recent Progress on Dynamics of a Special Arithmetic Function (C-H Jia); Some Diophantine Problems Arising from the Isomorphism Problem of Generic Polynomials (A Hoshi & K Miyake); A Statistical Relation of Roots of a Polynomial in Different Local Fields II (Y Kitaoka); Generalized Modular Functions and Their Fourier Coefficients (W Kohnen); Functional Relations for Zeta-Functions of Root Systems (Y Komori et al.); A Quick Introduction to Maass Forms (J-Y Liu); The Number of Non-Zero Coefficients of a Polynomial-Solved and Unsolved Problems (A Schinzel); Open Problems on Exponential and Character Sums (I E Shparlinski); Errata to OC A General Modular Relation in Analytic Number TheoryOCO (H Tsukada); Bibliography on Determinantal Expressions of Relative Class Numbers of Imaginary Abelian Number Fields (K Yamamura). Readership: Graduate students and researchers in mathematics.
Download or read book Further Progress in Analysis written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Further Progress in Analysis written by International Society for Analysis, Applications, and Computation. Congress and published by World Scientific. This book was released on 2009 with total page 877 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ISAAC (International Society for Analysis, its Applications and Computation) Congress, which has been held every second year since 1997, covers the major progress in analysis, applications and computation in recent years. In this proceedings volume, plenary lectures highlight the recent research results, while 17 sessions organized by well-known specialists reflect the state of the art of important subfields. This volume concentrates on partial differential equations, function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, inverse problems, functional differential and difference equations and integrable systems.
Download or read book Number Theory in Memory of Eduard Wirsing written by Helmut Maier and published by Springer Nature. This book was released on 2023-08-28 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eduard Wirsing was an outstanding number theorist. In his research he made significant contributions to various subfields of number theory and also collaborated with other eminent scientists (e.g., with the Fields Medalist Alan Baker as well as Don Zagier). This commemorative volume includes numerous papers on current research in number theory by well-known experts, as well as some personal recollections by companions of Wirsing. The topics covered in this volume include arithmetical functions, continued fractions, elementary proofs of the prime number theorem, friable integers, the Goldbach problem, Dirichlet series, Euler products, and more. There is something for every interested reader.
Download or read book Algorithmic Number Theory written by J. P. Buhler and published by Cambridge University Press. This book was released on 2008-10-20 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to number theory for beginning graduate students with articles by the leading experts in the field.
