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Heckes Theory Of Modular Forms And Dirichlet Series
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Book Synopsis Hecke's Theory of Modular Forms and Dirichlet Series by : Bruce C. Berndt
Download or read book Hecke's Theory of Modular Forms and Dirichlet Series written by Bruce C. Berndt and published by World Scientific. This book was released on 2008 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cyber security, encompassing both information and network security, is of utmost importance in today's information age. Cyber Security Standards, Practices and Industrial Applications: Systems and Methodologies details the latest and most important advances in security standards. First, it introduces the differences between information security (covers the understanding of security requirements, classification of threats, attacks and information protection systems and methodologies) and network security (includes both security protocols as well as systems which create a security perimeter around networks for intrusion detection and avoidance). In addition, the book serves as an essential reference to students, researchers, practitioners, and consultants in the area of social media, cyber security and information, and communication technologies (ICT).
Book Synopsis Modular Functions and Dirichlet Series in Number Theory by : Tom M. Apostol
Download or read book Modular Functions and Dirichlet Series in Number Theory written by Tom M. Apostol and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Modular Forms and Hecke Operators by : A. N. Andrianov
Download or read book Modular Forms and Hecke Operators written by A. N. Andrianov and published by American Mathematical Soc.. This book was released on 2016-01-29 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: he concept of Hecke operators was so simple and natural that, soon after Hecke's work, scholars made the attempt to develop a Hecke theory for modular forms, such as Siegel modular forms. As this theory developed, the Hecke operators on spaces of modular forms in several variables were found to have arithmetic meaning. Specifically, the theory provided a framework for discovering certain multiplicative properties of the number of integer representations of quadratic forms by quadratic forms. Now that the theory has matured, the time is right for this detailed and systematic exposition of its fundamental methods and results. Features: The book starts with the basics and ends with the latest results, explaining the current status of the theory of Hecke operators on spaces of holomorphic modular forms of integer and half-integer weight congruence-subgroups of integral symplectic groups.Hecke operators are considered principally as an instrument for studying the multiplicative properties of the Fourier coefficients of modular forms. It is the authors' intent that Modular Forms and Hecke Operators help attract young researchers to this beautiful and mysterious realm of number theory.
Book Synopsis Introduction to Siegel Modular Forms and Dirichlet Series by : Anatoli Andrianov
Download or read book Introduction to Siegel Modular Forms and Dirichlet Series written by Anatoli Andrianov and published by Springer Science & Business Media. This book was released on 2010-03-17 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Modular Forms by : Toshitsune Miyake
Download or read book Modular Forms written by Toshitsune Miyake and published by Springer Science & Business Media. This book was released on 2006-02-17 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a translation of the earlier book written by Koji Doi and the author, who revised it substantially for this English edition. It offers the basic knowledge of elliptic modular forms necessary to understand recent developments in number theory. It also treats the unit groups of quaternion algebras, rarely dealt with in books; and in the last chapter, Eisenstein series with parameter are discussed following the recent work of Shimura.
Book Synopsis Problems in the Theory of Modular Forms by : M. Ram Murty
Download or read book Problems in the Theory of Modular Forms written by M. Ram Murty and published by Springer. This book was released on 2016-11-25 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to the fascinating world of modular forms through a problem-solving approach. As such, besides researchers, the book can be used by the undergraduate and graduate students for self-instruction. The topics covered include q-series, the modular group, the upper half-plane, modular forms of level one and higher level, the Ramanujan τ-function, the Petersson inner product, Hecke operators, Dirichlet series attached to modular forms and further special topics. It can be viewed as a gentle introduction for a deeper study of the subject. Thus, it is ideal for non-experts seeking an entry into the field.
Book Synopsis Hecke's Theory of Modular Forms and Dirichlet Series by : Bruce C. Berndt
Download or read book Hecke's Theory of Modular Forms and Dirichlet Series written by Bruce C. Berndt and published by . This book was released on 1970* with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Modular Functions and Dirichlet Series in Number Theory by : Tom M. Apostol
Download or read book Modular Functions and Dirichlet Series in Number Theory written by Tom M. Apostol and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Modular Forms by : Serge Lang
Download or read book Introduction to Modular Forms written by Serge Lang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This book gives a thorough introduction to several theories that are fundamental to research on modular forms. Most of the material, despite its importance, had previously been unavailable in textbook form. Complete and readable proofs are given... In conclusion, this book is a welcome addition to the literature for the growing number of students and mathematicians in other fields who want to understand the recent developments in the theory of modular forms." #Mathematical Reviews# "This book will certainly be indispensable to all those wishing to get an up-to-date initiation to the theory of modular forms." #Publicationes Mathematicae#
Book Synopsis Modular Forms and Dirichlet Series by : Andrew Ogg
Download or read book Modular Forms and Dirichlet Series written by Andrew Ogg and published by . This book was released on 1969-01 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Elementary Dirichlet Series and Modular Forms by : Goro Shimura
Download or read book Elementary Dirichlet Series and Modular Forms written by Goro Shimura and published by Springer Science & Business Media. This book was released on 2007-08-06 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author :A. N. Andrianov V. G. Zhuravlev Publisher :American Mathematical Soc. ISBN 13 :9780821897621 Total Pages :350 pages Book Rating :4.8/5 (976 download)
Book Synopsis Modular forms and Hecke operators by : A. N. Andrianov V. G. Zhuravlev
Download or read book Modular forms and Hecke operators written by A. N. Andrianov V. G. Zhuravlev and published by American Mathematical Soc.. This book was released on 1995-08-28 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of Hecke operators was so simple and natural that, soon after Hecke's work, scholars made the attempt to develop a Hecke theory for modular forms, such as Siegel modular forms. As this theory developed, the Hecke operators on spaces of modular forms in several variables were found to have arithmetic meaning. Specifically, the theory provided a framework for discovering certain multiplicative properties of the number of integer representations of quadratic forms by quadratic forms. Now that the theory has matured, the time is right for this detailed and systematic exposition of its fundamental methods and results. Features: The book starts with the basics and ends with the latest results, explaining the current status of the theory of Hecke operators on spaces of holomorphic modular forms of integer and half-integer weight congruence-subgroups of integral symplectic groups. Hecke operators are considered principally as an instrument for studying the multiplicative properties of the Fourier coefficients of modular forms. It is the authors' intent that Modular Forms and Hecke Operators help attract young researchers to this beautiful and mysterious realm of number theory.
Book Synopsis Lectures on Dirichlet Series, Modular Functions and Quadratic Forms; Spring Term, 1938 by : Erich Hecke
Download or read book Lectures on Dirichlet Series, Modular Functions and Quadratic Forms; Spring Term, 1938 written by Erich Hecke and published by . This book was released on 1938 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Modular Forms: Basics and Beyond by : Goro Shimura
Download or read book Modular Forms: Basics and Beyond written by Goro Shimura and published by Springer Science & Business Media. This book was released on 2011-11-18 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an advanced book on modular forms. While there are many books published about modular forms, they are written at an elementary level, and not so interesting from the viewpoint of a reader who already knows the basics. This book offers something new, which may satisfy the desire of such a reader. However, we state every definition and every essential fact concerning classical modular forms of one variable. One of the principal new features of this book is the theory of modular forms of half-integral weight, another being the discussion of theta functions and Eisenstein series of holomorphic and nonholomorphic types. Thus the book is presented so that the reader can learn such theories systematically.
Author :Lloyd James Peter Kilford Publisher :World Scientific Publishing Company ISBN 13 :1783265477 Total Pages :252 pages Book Rating :4.7/5 (832 download)
Book Synopsis Modular Forms: A Classical And Computational Introduction (2nd Edition) by : Lloyd James Peter Kilford
Download or read book Modular Forms: A Classical And Computational Introduction (2nd Edition) written by Lloyd James Peter Kilford and published by World Scientific Publishing Company. This book was released on 2015-03-12 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modular Forms is a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to various subjects, such as the theory of quadratic forms, the proof of Fermat's Last Theorem and the approximation of π. The text gives a balanced overview of both the theoretical and computational sides of its subject, allowing a variety of courses to be taught from it.This second edition has been revised and updated. New material on the future of modular forms as well as a chapter about longer-form projects for students has also been added.
Book Synopsis Modular Forms, a Computational Approach by : William A. Stein
Download or read book Modular Forms, a Computational Approach written by William A. Stein and published by American Mathematical Soc.. This book was released on 2007-02-13 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This marvellous and highly original book fills a significant gap in the extensive literature on classical modular forms. This is not just yet another introductory text to this theory, though it could certainly be used as such in conjunction with more traditional treatments. Its novelty lies in its computational emphasis throughout: Stein not only defines what modular forms are, but shows in illuminating detail how one can compute everything about them in practice. This is illustrated throughout the book with examples from his own (entirely free) software package SAGE, which really bring the subject to life while not detracting in any way from its theoretical beauty. The author is the leading expert in computations with modular forms, and what he says on this subject is all tried and tested and based on his extensive experience. As well as being an invaluable companion to those learning the theory in a more traditional way, this book will be a great help to those who wish to use modular forms in applications, such as in the explicit solution of Diophantine equations. There is also a useful Appendix by Gunnells on extensions to more general modular forms, which has enough in it to inspire many PhD theses for years to come. While the book's main readership will be graduate students in number theory, it will also be accessible to advanced undergraduates and useful to both specialists and non-specialists in number theory. --John E. Cremona, University of Nottingham William Stein is an associate professor of mathematics at the University of Washington at Seattle. He earned a PhD in mathematics from UC Berkeley and has held positions at Harvard University and UC San Diego. His current research interests lie in modular forms, elliptic curves, and computational mathematics.
Book Synopsis Lectures by Erich Hecke on Dirichlet Series, Modular Functions and Quadratic Form by : Erich Hecke
Download or read book Lectures by Erich Hecke on Dirichlet Series, Modular Functions and Quadratic Form written by Erich Hecke and published by . This book was released on 1938 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
