Jacobi Forms, Finite Quadratic Modules and Weil Representations over Number Fields / by Hatice Boylan.

Format:

Book

Author/Creator:

Boylan, Hatice, author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 2130.

Lecture Notes in Mathematics, 0075-8434 ; 2130

Language:

English

Subjects (All):

Number theory.

Number Theory.

Local Subjects:

Number Theory.

Physical Description:

1 online resource (XIX, 130 pages).

Contained In:

Springer eBooks

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2015.

System Details:

text file PDF

Summary:

The new theory of Jacobi forms over totally real number fields introduced in this monograph is expected to give further insight into the arithmetic theory of Hilbert modular forms, its L-series, and into elliptic curves over number fields. This work is inspired by the classical theory of Jacobi forms over the rational numbers, which is an indispensable tool in the arithmetic theory of elliptic modular forms, elliptic curves, and in many other disciplines in mathematics and physics. Jacobi forms can be viewed as vector valued modular forms which take values in so-called Weil representations. Accordingly, the first two chapters develop the theory of finite quadratic modules and associated Weil representations over number fields. This part might also be interesting for those who are merely interested in the representation theory of Hilbert modular groups. One of the main applications is the complete classification of Jacobi forms of singular weight over an arbitrary totally real number field.

Contents:

Introduction

Notations

Finite Quadratic Modules

Weil Representations of Finite Quadratic Modules

Jacobi Forms over Totally Real Number Fields

Singular Jacobi Forms

Tables

Glossary.

Other Format:

Printed edition:

ISBN:

9783319129167

Access Restriction:

Restricted for use by site license.