Distribution Of Integral Fourier Coefficients Of A Modular Form Of Half Integral Weight Modulo Primes PDF Download
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Total Pages | : |
Release | : 2007 |
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Download Distribution of Integral Fourier Coefficients of a Modular Form of Half Integral Weight Modulo Primes Book in PDF, ePub and Kindle
Recently, Bruinier and Ono classified cusp forms $f(z) := \sum_{n=0}^{\infty} a_f(n)q ^n \in S_{\lambda+1/2}(\Gamma_0(N), \chi)\cap \mathbb{Z}[[q]]$ that does not satisfy a certain distribution property for modulo odd primes $p$. In this paper, using Rankin-Cohen Bracket, we extend this result to modular forms of half integral weight for primes $p \geq 5$. As applications of our main theorem we derive distribution properties, for modulo primes $p\geq5$, of traces of singular moduli and Hurwitz class number. We also study an analogue of Newman's conjecture for overpartitions.
Author | : W. Kohnen |
Publisher | : |
Total Pages | : 39 |
Release | : 1984 |
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Download Fourier Coefficients of Modular Forms of Half-integral Weight Book in PDF, ePub and Kindle
Author | : William Duke |
Publisher | : American Mathematical Soc. |
Total Pages | : 270 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 9780821843079 |
Download Analytic Number Theory Book in PDF, ePub and Kindle
Articles in this volume are based on talks given at the Gauss-Dirichlet Conference held in Gottingen on June 20-24, 2005. The conference commemorated the 150th anniversary of the death of C.-F. Gauss and the 200th anniversary of the birth of J.-L. Dirichlet. The volume begins with a definitive summary of the life and work of Dirichlet and continues with thirteen papers by leading experts on research topics of current interest in number theory that were directly influenced by Gauss and Dirichlet. Among the topics are the distribution of primes (long arithmetic progressions of primes and small gaps between primes), class groups of binary quadratic forms, various aspects of the theory of $L$-functions, the theory of modular forms, and the study of rational and integral solutions to polynomial equations in several variables. Information for our distributors: Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
Author | : Kamal Khuri-Makdisi |
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Total Pages | : 156 |
Release | : 1993 |
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Download Relations Between Fourier Coefficients of Nonholomorphic Hilbert Modular Forms of Half-integral Weight and Special Values of Dirichlet Series Book in PDF, ePub and Kindle
Author | : Xiangdong Wang |
Publisher | : |
Total Pages | : 18 |
Release | : 1993 |
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ISBN | : |
Download Fourier Coefficients of Cusp Forms with Half-integral Weight Book in PDF, ePub and Kindle
Author | : Henryk Iwaniec |
Publisher | : American Mathematical Soc. |
Total Pages | : 615 |
Release | : 2021-10-14 |
Genre | : Education |
ISBN | : 1470467704 |
Download Analytic Number Theory Book in PDF, ePub and Kindle
Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results. One of the primary attractions of this theory is its vast diversity of concepts and methods. The main goals of this book are to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, beautiful theorems, and powerful techniques. The book is written with graduate students in mind, and the authors nicely balance clarity, completeness, and generality. The exercises in each section serve dual purposes, some intended to improve readers' understanding of the subject and others providing additional information. Formal prerequisites for the major part of the book do not go beyond calculus, complex analysis, integration, and Fourier series and integrals. In later chapters automorphic forms become important, with much of the necessary information about them included in two survey chapters.
Author | : Bruce Berndt |
Publisher | : CRC Press |
Total Pages | : 368 |
Release | : 2002-11-20 |
Genre | : Mathematics |
ISBN | : 1000065286 |
Download Surveys in Number Theory Book in PDF, ePub and Kindle
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.
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Total Pages | : 984 |
Release | : 2007 |
Genre | : Mathematics |
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Download Mathematical Reviews Book in PDF, ePub and Kindle
Author | : Bruce C. Berndt |
Publisher | : Springer Science & Business Media |
Total Pages | : 453 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461240867 |
Download Analytic Number Theory Book in PDF, ePub and Kindle
On May 16 -20, 1995, approximately 150 mathematicians gathered at the Conference Center of the University of Illinois at Allerton Park for an Inter national Conference on Analytic Number Theory. The meeting marked the approaching official retirement of Heini Halberstam from the mathematics fac ulty of the University of Illinois at Urbana-Champaign. Professor Halberstam has been at the University since 1980, for 8 years as head of the Department of Mathematics, and has been a leading researcher and teacher in number theory for over forty years. The program included invited one hour lectures by G. Andrews, J. Bour gain, J. M. Deshouillers, H. Halberstam, D. R. Heath-Brown, H. Iwaniec, H. L. Montgomery, R. Murty, C. Pomerance, and R. C. Vaughan, and almost one hundred other talks of varying lengths. These volumes comprise contributions from most of the principal speakers and from many of the other participants, as well as some papers from mathematicians who were unable to attend. The contents span a broad range of themes from contemporary number theory, with the majority having an analytic flavor.
Author | : John B. Friedlander |
Publisher | : American Mathematical Soc. |
Total Pages | : 554 |
Release | : 2010-06-22 |
Genre | : Mathematics |
ISBN | : 0821849700 |
Download Opera de Cribro Book in PDF, ePub and Kindle
This is a true masterpiece that will prove to be indispensable to the serious researcher for many years to come. --Enrico Bombieri, Institute for Advanced Study This is a truly comprehensive account of sieves and their applications, by two of the world's greatest authorities. Beginners will find a thorough introduction to the subject, with plenty of helpful motivation. The more practised reader will appreciate the authors' insights into some of the more mysterious parts of the theory, as well as the wealth of new examples. --Roger Heath-Brown, University of Oxford, Fellow of Royal Society This is a comprehensive and up-to-date treatment of sieve methods. The theory of the sieve is developed thoroughly with complete and accessible proofs of the basic theorems. Included is a wide range of applications, both to traditional questions such as those concerning primes, and to areas previously unexplored by sieve methods, such as elliptic curves, points on cubic surfaces and quantum ergodicity. New proofs are given also of some of the central theorems of analytic number theory; these proofs emphasize and take advantage of the applicability of sieve ideas. The book contains numerous comments which provide the reader with insight into the workings of the subject, both as to what the sieve can do and what it cannot do. The authors reveal recent developements by which the parity barrier can be breached, exposing golden nuggets of the subject, previously inaccessible. The variety in the topics covered and in the levels of difficulty encountered makes this a work of value to novices and experts alike, both as an educational tool and a basic reference.