**Memoirs of the American Mathematical Society**

2015;
64 pp;
Softcover

MSC: Primary 11;

Print ISBN: 978-1-4704-1419-1

Product Code: MEMO/237/1117

List Price: $68.00

Individual Member Price: $40.80

**Electronic ISBN: 978-1-4704-2501-2
Product Code: MEMO/237/1117.E**

List Price: $68.00

Individual Member Price: $40.80

# Brandt Matrices and Theta Series over Global Function Fields

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*Chih-Yun Chuang; Ting-Fang Lee; Fu-Tsun Wei; Jing Yu*

The aim of this article is to give a complete account of the Eichler-Brandt theory over function fields and the basis problem for Drinfeld type automorphic forms. Given arbitrary function field \(k\) together with a fixed place \(\infty\), the authors construct a family of theta series from the norm forms of “definite” quaternion algebras, and establish an explicit Hecke-module homomorphism from the Picard group of an associated definite Shimura curve to a space of Drinfeld type automorphic forms. The “compatibility” of these homomorphisms with different square-free levels is also examined. These Hecke-equivariant maps lead to a nice description of the subspace generated by the authors' theta series, and thereby contributes to the so-called basis problem.

Restricting the norm forms to pure quaternions, the authors obtain another family of theta series which are automorphic functions on the metaplectic group, and this results in a Shintani-type correspondence between Drinfeld type forms and metaplectic forms.

#### Table of Contents

# Table of Contents

## Brandt Matrices and Theta Series over Global Function Fields

- Cover Cover11 free
- Title page i2 free
- Chapter 1. Introduction 18 free
- Chapter 2. Brandt matrices and definite Shimura curves 714 free
- Chapter 3. The basis problem for Drinfeld type automorphic forms 1724
- Chapter 4. Metaplectic forms and Shintani-type correspondence 3340
- Chapter 5. Trace formula of Brandt matrices 5158
- Bibliography 6168
- Symbols 6370
- Back Cover Back Cover176