Download or read book Lectures on a Method in the Theory of Exponential Sums written by M. Jutila and published by . This book was released on 1987 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Van Der Corput s Method of Exponential Sums written by S. W. Graham and published by Cambridge University Press. This book was released on 1991-01-25 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a self-contained account of the one- and two-dimensional van der Corput method and its use in estimating exponential sums. These arise in many problems in analytic number theory. It is the first cohesive account of much of this material and will be welcomed by graduates and professionals in analytic number theory. The authors show how the method can be applied to problems such as upper bounds for the Riemann-Zeta function. the Dirichlet divisor problem, the distribution of square free numbers, and the Piatetski-Shapiro prime number theorem.
Download or read book Area Lattice Points and Exponential Sums written by M. N. Huxley and published by Clarendon Press. This book was released on 1996-06-13 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: In analytic number theory a large number of problems can be "reduced" to problems involving the estimation of exponential sums in one or several variables. This book is a thorough treatment of the developments arising from the method developed by Bombieri and Iwaniec in 1986 for estimating the Riemann zeta function on the line *s = 1/2. Huxley and his coworkers (mostly Huxley) have taken this method and vastly extended and improved it. The powerful techniques presented here go considerably beyond older methods for estimating exponential sums such as van de Corput's method. The potential for the method is far from being exhausted, and there is considerable motivation for other researchers to try to master this subject. However, anyone currently trying to learn all of this material has the formidable task of wading through numerous papers in the literature. This book simplifies that task by presenting all of the relevant literature and a good part of the background in one package. The audience for the book will be mathematics graduate students and faculties with a research interest in analytic theory; more specifically, those with an interest in exponential sum methods. The book is self-contained; any graduate student with a one semester course in analytic number theory should have a more than sufficient background.
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 Lectures on a Method in the Theory of Exponential Sums written by Matti Jutila and published by Springer Verlag. This book was released on 1987 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on a Method in the Theory of Exponential Sums written by Matti I. Jutila and published by Springer. This book was released on 1988-02-19 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are based on the lectures given by the author at the Tata Institute in 1985 on certain classes of exponential sums and their applications in analytic number theory. More specifically, the exponential sums under consideration involve either the divisor function d(n) or Fourier coefficients of cusp forms (e.g. Ramanujan's function #3(n)). However, the "transformation method" presented, relying on general principles such as functional equations, summation formulae and the saddle point method, has a wider scope. Its classical analogue is the familiar "process B" in van der Corput's method, that transforms ordinary exponential sums by Poisson's summation formula and the saddle point method. In the present context, the summation formulae required are of the Voronoi type. These are derived in Chapter I. Chapter II deals with exponential integrals and the saddle point method. The main results of these notes, the general transformation formulae for exponential sums, are then established in Chapter III and some applications are given in Chapter IV. First the transformation of Dirichlet polynomials is worked out in detail, and the rest of the chapter is devoted to estimations of exponential sums and Dirichlet series. The material in Chapters III and IV appears here for the first time in print. The notes are addressed to researchers but are also accessible to graduate students with some basic knowledge of analytic number theory.
Download or read book Multiple Dirichlet Series Automorphic Forms and Analytic Number Theory written by Solomon Friedberg and published by American Mathematical Soc.. This book was released on 2006 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiple Dirichlet series are Dirichlet series in several complex variables. A multiple Dirichlet series is said to be perfect if it satisfies a finite group of functional equations and has meromorphic continuation everywhere. The earliest examples came from Mellin transforms of metaplectic Eisenstein series and have been intensively studied over the last twenty years. More recently, many other examples have been discovered and it appears that all the classical theorems on moments of $L$-functions as well as the conjectures (such as those predicted by random matrix theory) can now be obtained via the theory of multiple Dirichlet series. Furthermore, new results, not obtainable by other methods, are just coming to light. This volume offers an account of some of the major research to date and the opportunities for the future. It includes an exposition of the main results in the theory of multiple Dirichlet series, and papers on moments of zeta- and $L$-functions, on new examples of multiple Dirichlet
Download or read book Number Theory written by Richard Mollin and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-12-19 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Download or read book Number Theory written by Hans P. Schlickewei and published by Springer. This book was released on 2006-11-14 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 15 papers of this selection of contributions to the Journées Arithmétiques 1987 include both survey articles and original research papers and represent a cross-section of topics such as Abelian varieties, algebraic integers, arithmetic algebraic geometry, additive number theory, computational number theory, exponential sums, modular forms, transcendence and Diophantine approximation, uniform distribution.
Download or read book Analytic and Probabilistic Methods in Number Theory written by E. Laurincikas and published by Walter de Gruyter. This book was released on 2012-02-14 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis written by Hugh L. Montgomery and published by American Mathematical Soc.. This book was released on 1994 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains lectures presented by Hugh L. Montgomery at the NSF-CBMS Regional Conference held at Kansas State University in May 1990. The book focuses on important topics in analytic number theory that involve ideas from harmonic analysis. One valuable aspect of the book is that it collects material that was either unpublished or that had appeared only in the research literature. This book would be an excellent resource for harmonic analysts interested in moving into research in analytic number theory. In addition, it is suitable as a textbook in an advanced graduate topics course in nu.
Download or read book Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis written by Hugh L. Montgomery and published by American Mathematical Soc.. This book was released on 1994 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains lectures presented by Hugh L. Montgomery at the NSF-CBMS Regional Conference held at Kansas State University in May 1990. The book focuses on important topics in analytic number theory that involve ideas from harmonic analysis. One particularly valuable aspect of the book is that it collects material that was either unpublished or that had appeared only in the research literature. The book should be a useful resource for harmonic analysts interested in moving into research in analytic number theory. In addition, it is suitable as a textbook in an advanced graduate topics course in number theory.
Download or read book Proceedings of the Amalfi Conference on Analytic Number Theory written by and published by . This book was released on 1992 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Proceedings of the International Congress of Mathematicians August 21 29 1990 Kyoto Japan written by Ichirō Satake and published by . This book was released on 1991 with total page 868 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Number Theory written by Matti Jutila and published by Walter de Gruyter. This book was released on 2014-01-02 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Proceedings contain 22 refereed research and survey articles based on lectures given at the Turku Symposium on Number Theory in Memory of Kustaa Inkeri, held in Turku, Finland, from May 31 to June 4, 1999. The subject of the symposium was number theory in a broad sense with an emphasis on recent advances and modern methods. The topics covered in this volume include various questions in elementary number theory, new developments in classical Diophantine problems - in particular of the Fermat and Catalan type, the ABC-conjecture, arithmetic algebraic geometry, elliptic curves, Diophantine approximations, Abelian fields, exponential sums, sieve methods, box splines, the Riemann zeta-function and other Dirichlet series, and the spectral theory of automorphic functions with its arithmetical applications.
Download or read book Encyclopaedia of Mathematics Supplement III written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2007-11-23 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.
