Modular Functions and Dirichlet Series in Number Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Modular Functions and Dirichlet Series in Number Theory write by Tom M. Apostol. This book was released on 2012-12-06. Modular Functions and Dirichlet Series in Number Theory available in PDF, EPUB and Kindle. A new edition of a classical treatment of elliptic and modular functions with some of their number-theoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for the Dedekind eta function. It covers many topics, such as Hecke’s theory of entire forms with multiplicative Fourier coefficients, and the last chapter recounts Bohr’s theory of equivalence of general Dirichlet series.
Modular Functions and Dirichlet Series in Number Theory
Modular Functions and Dirichlet Series in Number Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Modular Functions and Dirichlet Series in Number Theory write by Tom M. Apostol. This book was released on 2012-12-06. Modular Functions and Dirichlet Series in Number Theory available in PDF, EPUB and Kindle. 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.
Modular Functions and Dirichlet Series in Number Theory
Modular Functions and Dirichlet Series in Number Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Modular Functions and Dirichlet Series in Number Theory write by Tom M. Apostol. This book was released on 1997-06-01. Modular Functions and Dirichlet Series in Number Theory available in PDF, EPUB and Kindle. A new edition of a classical treatment of elliptic and modular functions with some of their number-theoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for the Dedekind eta function. It covers many topics, such as Hecke’s theory of entire forms with multiplicative Fourier coefficients, and the last chapter recounts Bohr’s theory of equivalence of general Dirichlet series.
Elementary Dirichlet Series and Modular Forms
Elementary Dirichlet Series and Modular Forms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elementary Dirichlet Series and Modular Forms write by Goro Shimura. This book was released on 2007-08-06. Elementary Dirichlet Series and Modular Forms available in PDF, EPUB and Kindle. A book on any mathematical subject beyond the textbook level is of little value unless it contains new ideas and new perspectives. It helps to include new results, provided that they give the reader new insights and are presented along with known old results in a clear exposition. It is with this philosophy that the author writes this volume. The two subjects, Dirichlet series and modular forms, are traditional subjects, but here they are treated in both orthodox and unorthodox ways. Regardless of the unorthodox treatment, the author has made the book accessible to those who are not familiar with such topics by including plenty of expository material.
Introduction to Siegel Modular Forms and Dirichlet Series
Introduction to Siegel Modular Forms and Dirichlet Series - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Siegel Modular Forms and Dirichlet Series write by Anatoli Andrianov. This book was released on 2010-03-17. Introduction to Siegel Modular Forms and Dirichlet Series available in PDF, EPUB and Kindle. Several years ago I was invited to an American university to give one-term graduate course on Siegel modular forms, Hecke operators, and related zeta functions. The idea to present in a concise but basically complete and self-contained form an int- duction to an important and developing area based partly on my own work attracted me. I accepted the invitation and started to prepare the course. Unfortunately, the visit was not realized. But the idea of such a course continued to be alive till after a number of years this book was ?nally completed. I hope that this short book will serve to attract young researchers to this beautiful ?eld, and that it will simplify and make more pleasant the initial steps. No special knowledge is presupposed for reading this book beyond standard courses in algebra and calculus (one and several variables), although some skill in working with mathematical texts would be helpful. The reader will judge whether the result was worth the effort. Dedications. The ideas of Goro Shimura exerted a deep in?uence on the number theory of the second half of the twentieth century in general and on the author’s formation in particular. When Andre ` Weil was signing a copy of his “Basic Number Theory” to my son, he wrote in Russian, ”To Fedor Anatolievich hoping that he will become a number theoretist”. Fedor has chosen computer science. Now I pass on the idea to Fedor’s daughter, Alexandra Fedorovna.
