Share

Modular Forms with Integral and Half-Integral Weights

2013-02-20 Mathematics
Download Modular Forms with Integral and Half-Integral Weights PDF Online Free

Author :
Release : 2013-02-20
Genre : Mathematics
Kind : eBook
Book Rating : 026/5 ( reviews)

GET EBOOK


Book Synopsis Modular Forms with Integral and Half-Integral Weights by : Xueli Wang

Download or read book Modular Forms with Integral and Half-Integral Weights written by Xueli Wang. This book was released on 2013-02-20. Available in PDF, EPUB and Kindle. Book excerpt: "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.

Modular Functions of One Variable, I-IV

1973 Modular functions
Download Modular Functions of One Variable, I-IV PDF Online Free

Author :
Release : 1973
Genre : Modular functions
Kind : eBook
Book Rating : /5 ( reviews)

GET EBOOK


Book Synopsis Modular Functions of One Variable, I-IV by : Willem Kuyk

Download or read book Modular Functions of One Variable, I-IV written by Willem Kuyk. This book was released on 1973. Available in PDF, EPUB and Kindle. Book excerpt:

The Theory of Jacobi Forms

2013-12-14 Mathematics
Download The Theory of Jacobi Forms PDF Online Free

Author :
Release : 2013-12-14
Genre : Mathematics
Kind : eBook
Book Rating : 628/5 ( reviews)

GET EBOOK


Book Synopsis The Theory of Jacobi Forms by : Martin Eichler

Download or read book The Theory of Jacobi Forms written by Martin Eichler. This book was released on 2013-12-14. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Some Applications of Modular Forms

1990-11-15 Mathematics
Download Some Applications of Modular Forms PDF Online Free

Author :
Release : 1990-11-15
Genre : Mathematics
Kind : eBook
Book Rating : 442/5 ( reviews)

GET EBOOK


Book Synopsis Some Applications of Modular Forms by : Peter Sarnak

Download or read book Some Applications of Modular Forms written by Peter Sarnak. This book was released on 1990-11-15. Available in PDF, EPUB and Kindle. Book excerpt: The theory of modular forms and especially the so-called 'Ramanujan Conjectures' have been applied to resolve problems in combinatorics, computer science, analysis and number theory. This tract, based on the Wittemore Lectures given at Yale University, is concerned with describing some of these applications. In order to keep the presentation reasonably self-contained, Professor Sarnak begins by developing the necessary background material in modular forms. He then considers the solution of three problems: the Ruziewicz problem concerning finitely additive rotationally invariant measures on the sphere; the explicit construction of highly connected but sparse graphs: 'expander graphs' and 'Ramanujan graphs'; and the Linnik problem concerning the distribution of integers that represent a given large integer as a sum of three squares. These applications are carried out in detail. The book therefore should be accessible to a wide audience of graduate students and researchers in mathematics and computer science.

Modular Forms: Basics and Beyond

2011-11-18 Mathematics
Download Modular Forms: Basics and Beyond PDF Online Free

Author :
Release : 2011-11-18
Genre : Mathematics
Kind : eBook
Book Rating : 25X/5 ( reviews)

GET EBOOK


Book Synopsis Modular Forms: Basics and Beyond by : Goro Shimura

Download or read book Modular Forms: Basics and Beyond written by Goro Shimura. This book was released on 2011-11-18. 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.

You may also like...