A Congruence From Dedekind Sums

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A Congruence From Dedekind Sums

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Author :
language : en
Publisher:
Release Date : 1979

A Congruence From Dedekind Sums written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Dedekind sums categories.

A Congruence From Dedekind Sums

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Author : Kenneth H. Rosen
language : en
Publisher:
Release Date : 1979

A Congruence From Dedekind Sums written by Kenneth H. Rosen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Dedekind sums categories.

Dedekind Sums

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Author : Hans Rademacher
language : en
Publisher: American Mathematical Soc.
Release Date : 1972-12-31

Dedekind Sums written by Hans Rademacher and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-12-31 with MATHEMATICS categories.

These notes from Hans Rademacher's 1963 Hedrick Lectures have been gently polished and augmented by Emil Grosswald. While the topic itself is specialized, these sums are linked in diverse ways to many results in number theory, elliptical modular functions, and topology. The first main result is a surprising reciprocity law that is equivalent to the law of quadratic reciprocity.

Asymptotics And Congruence Properties For Stanley S Partition Function And A Note On A Theorem Of Koike

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Author : Holly Marie Swisher
language : en
Publisher:
Release Date : 2005

Asymptotics And Congruence Properties For Stanley S Partition Function And A Note On A Theorem Of Koike written by Holly Marie Swisher and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.

Number Theory

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Author : Richard Mollin
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-12-19

Number Theory written by Richard Mollin and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-19 with Mathematics categories.

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.

Modular Functions And Dirichlet Series In Number Theory

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Author : Tom M. Apostol
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Modular Functions And Dirichlet Series In Number Theory written by Tom M. Apostol and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This is the second volume of a 2-volume textbook* which evolved from a course (Mathematics 160) offered at the California Institute of Technology du ring the last 25 years. The second volume presupposes a background in number theory com parable to that provided in the first volume, together with a knowledge of the basic concepts of complex analysis. Most of the present volume is devoted to elliptic functions and modular functions with some of their number-theoretic applications. Among the major topics treated are Rademacher's convergent series for the partition function, Lehner's congruences for the Fourier coefficients of the modular functionj( r), and Hecke's theory of entire forms with multiplicative Fourier coefficients. The last chapter gives an account of Bohr's theory of equivalence of general Dirichlet series. Both volumes of this work emphasize classical aspects of a subject wh ich in recent years has undergone a great deal of modern development. It is hoped that these volumes will help the nonspecialist become acquainted with an important and fascinating part of mathematics and, at the same time, will provide some of the background that belongs to the repertory of every specialist in the field. This volume, like the first, is dedicated to the students who have taken this course and have gone on to make notable contributions to number theory and other parts of mathematics. T. M. A. January, 1976 * The first volume is in the Springer-Verlag series Undergraduate Texts in Mathematics under the title Introduction to Analytic Number Theory.

Theory Of Algebraic Integers

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Author : Richard Dedekind
language : en
Publisher: Cambridge University Press
Release Date : 1996-09-28

Theory Of Algebraic Integers written by Richard Dedekind and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-09-28 with Mathematics categories.

A translation of a classic work by one of the truly great figures of mathematics.

On Questions Of Congruence And Size For Modular Forms And Maass Poincar Series

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Author : Sharon Anne Garthwaite
language : en
Publisher:
Release Date : 2007

On Questions Of Congruence And Size For Modular Forms And Maass Poincar Series written by Sharon Anne Garthwaite and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.

Recent Progress On Topics Of Ramanujan Sums And Cotangent Sums Associated With The Riemann Hypothesis

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Author : Helmut Maier
language : en
Publisher: World Scientific
Release Date : 2021-12-28

Recent Progress On Topics Of Ramanujan Sums And Cotangent Sums Associated With The Riemann Hypothesis written by Helmut Maier and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-28 with Mathematics categories.

In this monograph, we study recent results on some categories of trigonometric/exponential sums along with various of their applications in Mathematical Analysis and Analytic Number Theory. Through the two chapters of this monograph, we wish to highlight the applicability and breadth of techniques of trigonometric/exponential sums in various problems focusing on the interplay of Mathematical Analysis and Analytic Number Theory. We wish to stress the point that the goal is not only to prove the desired results, but also to present a plethora of intermediate Propositions and Corollaries investigating the behaviour of such sums, which can also be applied in completely different problems and settings than the ones treated within this monograph.In the present work we mainly focus on the applications of trigonometric/exponential sums in the study of Ramanujan sums — which constitute a very classical domain of research in Number Theory — as well as the study of certain cotangent sums with a wide range of applications, especially in the study of Dedekind sums and a facet of the research conducted on the Riemann Hypothesis. For example, in our study of the cotangent sums treated within the second chapter, the methods and techniques employed reveal unexpected connections with independent and very interesting problems investigated in the past by R de la Bretèche and G Tenenbaum on trigonometric series, as well as by S Marmi, P Moussa and J-C Yoccoz on Dynamical Systems.Overall, a reader who has mastered fundamentals of Mathematical Analysis, as well as having a working knowledge of Classical and Analytic Number Theory, will be able to gradually follow all the parts of the monograph. Therefore, the present monograph will be of interest to advanced undergraduate and graduate students as well as researchers who wish to be informed on the latest developments on the topics treated.

Galois Theory And Modular Forms

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Author : Ki-ichiro Hashimoto
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01

Galois Theory And Modular Forms written by Ki-ichiro Hashimoto and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.

This volume is an outgrowth of the research project "The Inverse Ga lois Problem and its Application to Number Theory" which was carried out in three academic years from 1999 to 2001 with the support of the Grant-in-Aid for Scientific Research (B) (1) No. 11440013. In September, 2001, an international conference "Galois Theory and Modular Forms" was held at Tokyo Metropolitan University after some preparatory work shops and symposia in previous years. The title of this book came from that of the conference, and the authors were participants of those meet All of the articles here were critically refereed by experts. Some of ings. these articles give well prepared surveys on branches of research areas, and many articles aim to bear the latest research results accompanied with carefully written expository introductions. When we started our re~earch project, we picked up three areas to investigate under the key word "Galois groups"; namely, "generic poly nomials" to be applied to number theory, "Galois coverings of algebraic curves" to study new type of representations of absolute Galois groups, and explicitly described "Shimura varieties" to understand well the Ga lois structures of some interesting polynomials including Brumer's sextic for the alternating group of degree 5. The topics of the articles in this volume are widely spread as a result. At a first glance, some readers may think this book somewhat unfocussed.