Fourier Coefficients Of Modular Forms Of Half Integral Weight PDF Download
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Author | : Xueli Wang |
Publisher | : Springer Science & Business Media |
Total Pages | : 436 |
Release | : 2013-02-20 |
Genre | : Mathematics |
ISBN | : 3642293026 |
Download Modular Forms with Integral and Half-Integral Weights Book in PDF, ePub and Kindle
"Modular Forms with Integral and Half-Integral Weights" focuses on the fundamental theory of modular forms of one variable with integral and half-integral weights. The main theme of the book is the theory of Eisenstein series. It is a fundamental problem to construct a basis of the orthogonal complement of the space of cusp forms; as is well known, this space is spanned by Eisenstein series for any weight greater than or equal to 2. The book proves that the conclusion holds true for weight 3/2 by explicitly constructing a basis of the orthogonal complement of the space of cusp forms. The problem for weight 1/2, which was solved by Serre and Stark, will also be discussed in this book. The book provides readers not only basic knowledge on this topic but also a general survey of modern investigation methods of modular forms with integral and half-integral weights. It will be of significant interest to researchers and practitioners in modular forms of mathematics. Dr. Xueli Wang is a Professor at South China Normal University, China. Dingyi Pei is a Professor at Guangzhou University, China.
Author | : W. Kohnen |
Publisher | : |
Total Pages | : 39 |
Release | : 1984 |
Genre | : |
ISBN | : |
Download Fourier Coefficients of Modular Forms of Half-integral Weight Book in PDF, ePub and Kindle
Author | : |
Publisher | : |
Total Pages | : |
Release | : 2007 |
Genre | : |
ISBN | : |
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 | : Xiangdong Wang |
Publisher | : |
Total Pages | : 18 |
Release | : 1993 |
Genre | : |
ISBN | : |
Download Fourier Coefficients of Cusp Forms with Half-integral Weight Book in PDF, ePub and Kindle
Author | : P. Guerzhoy |
Publisher | : |
Total Pages | : 11 |
Release | : 1995 |
Genre | : |
ISBN | : |
Download A P-acid Property of Fourier Coefficients of Modular Forms of Half Integral Weight Book in PDF, ePub and Kindle
Author | : P. Guerzhoy |
Publisher | : |
Total Pages | : 11 |
Release | : 1995 |
Genre | : |
ISBN | : |
Download A P-adic Property of Fourier Coefficients of Modular Forms of Half Integral Weight Book in PDF, ePub and Kindle
Author | : Ken Ono |
Publisher | : American Mathematical Soc. |
Total Pages | : 226 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 0821833685 |
Download The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and $q$-series Book in PDF, ePub and Kindle
Chapter 1.
Author | : Kamal Khuri-Makdisi |
Publisher | : |
Total Pages | : 156 |
Release | : 1993 |
Genre | : |
ISBN | : |
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 | : A. N. Andrianov |
Publisher | : American Mathematical Soc. |
Total Pages | : 346 |
Release | : 2016-01-29 |
Genre | : |
ISBN | : 1470418681 |
Download Modular Forms and Hecke Operators Book in PDF, ePub and Kindle
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.
Author | : Jan Hendrik Bruinier |
Publisher | : |
Total Pages | : 17 |
Release | : 1997 |
Genre | : |
ISBN | : |
Download Non-vanishing Modulo L of Fourier Coefficients of Half-integral Weight Modular Forms Book in PDF, ePub and Kindle