Modular Forms With Integral And Half Integral Weights 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 | : Martin Eichler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 156 |
| Release | : 2013-12-14 |
| Genre | : Mathematics |
| ISBN | : 1468491628 |
Download The Theory of Jacobi Forms Book in PDF, ePub and Kindle
The functions studied in this monogra9h are a cross between elliptic functions and modular forms in one variable. Specifically, we define a Jacobi form on SL (~) to be a holomorphic function 2 (JC = upper half-plane) satisfying the t\-10 transformation eouations 2Tiimcz· k CT +d a-r +b z) (1) ((cT+d) e cp(T, z) cp CT +d ' CT +d (2) rjl(T, z+h+]l) and having a Four·ier expansion of the form 00 e2Tii(nT +rz) (3) cp(T, z) 2: c(n, r) 2:: rE~ n=O 2 r ~ 4nm Here k and m are natural numbers, called the weight and index of rp, respectively. Note that th e function cp (T, 0) is an ordinary modular formofweight k, whileforfixed T thefunction z-+rjl( -r, z) isa function of the type normally used to embed the elliptic curve ~/~T + ~ into a projective space. If m= 0, then cp is independent of z and the definition reduces to the usual notion of modular forms in one variable. We give three other examples of situations where functions satisfying (1)-(3) arise classically: 1. Theta series. Let Q: ~-+ ~ be a positive definite integer valued quadratic form and B the associated bilinear form.
| Author | : Goro Shimura |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 183 |
| Release | : 2011-11-18 |
| Genre | : Mathematics |
| ISBN | : 146142125X |
Download Modular Forms: Basics and Beyond Book in PDF, ePub and Kindle
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 | : Willem Kuyk |
| Publisher | : Springer |
| Total Pages | : 210 |
| Release | : 1973 |
| Genre | : Mathematics |
| ISBN | : |
Download Modular Functions of One Variable, I-IV Book in PDF, ePub and Kindle
| Author | : YoungJu Choie |
| Publisher | : Springer Nature |
| Total Pages | : 296 |
| Release | : 2019-11-20 |
| Genre | : Mathematics |
| ISBN | : 3030291235 |
Download Jacobi-Like Forms, Pseudodifferential Operators, and Quasimodular Forms Book in PDF, ePub and Kindle
This book explores various properties of quasimodular forms, especially their connections with Jacobi-like forms and automorphic pseudodifferential operators. The material that is essential to the subject is presented in sufficient detail, including necessary background on pseudodifferential operators, Lie algebras, etc., to make it accessible also to non-specialists. The book also covers a sufficiently broad range of illustrations of how the main themes of the book have occurred in various parts of mathematics to make it attractive to a wider audience. The book is intended for researchers and graduate students in number theory.
| 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 | : L J P Kilford |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 252 |
| Release | : 2015-03-12 |
| Genre | : Mathematics |
| ISBN | : 1783265477 |
Download Modular Forms Book in PDF, ePub and Kindle
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.
| Author | : Jan Hendrik Bruinier |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 273 |
| Release | : 2008-02-10 |
| Genre | : Mathematics |
| ISBN | : 3540741194 |
Download The 1-2-3 of Modular Forms Book in PDF, ePub and Kindle
This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.
| Author | : V. Vatsal |
| Publisher | : American Mathematical Society |
| Total Pages | : 108 |
| Release | : 2023-09-27 |
| Genre | : Mathematics |
| ISBN | : 1470465507 |
Download Toric Periods and $p$-adic Families of Modular Forms of Half-Integral Weight Book in PDF, ePub and Kindle
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| Author | : Ameya Pitale |
| Publisher | : Springer |
| Total Pages | : 138 |
| Release | : 2019-05-07 |
| Genre | : Mathematics |
| ISBN | : 3030156753 |
Download Siegel Modular Forms Book in PDF, ePub and Kindle
This monograph introduces two approaches to studying Siegel modular forms: the classical approach as holomorphic functions on the Siegel upper half space, and the approach via representation theory on the symplectic group. By illustrating the interconnections shared by the two, this book fills an important gap in the existing literature on modular forms. It begins by establishing the basics of the classical theory of Siegel modular forms, and then details more advanced topics. After this, much of the basic local representation theory is presented. Exercises are featured heavily throughout the volume, the solutions of which are helpfully provided in an appendix. Other topics considered include Hecke theory, Fourier coefficients, cuspidal automorphic representations, Bessel models, and integral representation. Graduate students and young researchers will find this volume particularly useful. It will also appeal to researchers in the area as a reference volume. Some knowledge of GL(2) theory is recommended, but there are a number of appendices included if the reader is not already familiar.
