Modular Forms and Functions

Robert A. Rankin

ISBN 10: 0521091683 / ISBN 13: 9780521091688

Published by Cambridge University Press, 2008

About this Item

Druck auf Anfrage Neuware - Printed after ordering - This book provides an introduction to the theory of elliptic modular functions and forms, a subject of increasing interest because of its connexions with the theory of elliptic curves. Modular forms are generalisations of functions like theta functions. They can be expressed as Fourier series, and the Fourier coefficients frequently possess multiplicative properties which lead to a correspondence between modular forms and Dirichlet series having Euler products. The Fourier coefficients also arise in certain representational problems in the theory of numbers, for example in the study of the number of ways in which a positive integer may be expressed as a sum of a given number of squares. The treatment of the theory presented here is fuller than is customary in a textbook on automorphic or modular forms, since it is not confined solely to modular forms of integral weight (dimension). It will be of interest to professional mathematicians as well as senior undergraduate and graduate students in pure mathematics.

Seller Inventory # 9780521091688

Bibliographic Details

• Title: Modular Forms and Functions
• Publisher: Cambridge University Press
• Publication Date: 2008
• Language: English
• ISBN 10: 0521091683
• ISBN 13: 9780521091688
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 229W x 152H x 23D millimeters 229 millimeters width by 152 millimeters height by 23 millimeters depth
• Weight: 647 grams

About this title

Synopsis

This book provides an introduction to the theory of elliptic modular functions and forms, a subject of increasing interest because of its connexions with the theory of elliptic curves. Modular forms are generalisations of functions like theta functions. They can be expressed as Fourier series, and the Fourier coefficients frequently possess multiplicative properties which lead to a correspondence between modular forms and Dirichlet series having Euler products. The Fourier coefficients also arise in certain representational problems in the theory of numbers, for example in the study of the number of ways in which a positive integer may be expressed as a sum of a given number of squares. The treatment of the theory presented here is fuller than is customary in a textbook on automorphic or modular forms, since it is not confined solely to modular forms of integral weight (dimension). It will be of interest to professional mathematicians as well as senior undergraduate and graduate students in pure mathematics.

Book Description

This book provides an introduction to the theory of elliptic modular functions and forms, a subject of increasing interest because of its connexions with the theory of elliptic curves. Modular forms are generalisations of functions like theta functions.