Brandt matrices and theta series over global function fields
Author(s)
Bibliographic Information
Brandt matrices and theta series over global function fields
（Memoirs of the American Mathematical Society, v. 237,
American Mathematical Society, 2015
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Other authors: Ting-Fang Lee, Fu-Tsun Wei, Jing Yu
Includes bibliographical references (p. 61)
Description and Table of Contents
Description
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
Introduction
Brandt matrices and definite Shimura curves
The basis problem for Drinfeld type automorphic forms
Metaplectic forms and Shintani-type correspondence
Trace formula of Brandt matrices
Bibliography
Symbols
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