Brandt matrices and theta series over global function fields
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 [infinity symbol], we 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. Th…
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- Full title :Brandt matrices and theta series over global function fields / Chih-Yun Chuang, Ting-Fang Lee, Fu-Tsun Wei, Jing Yu.
Summary
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 [infinity symbol], we 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 our theta series, and thereby contributes to the so-called basis problem. Restricting the norm forms to pure quaternions, we obtain another family of theta series which are automorphic functions on the metaplectic group, and results in a Shintani-type correspondence between Drinfeld type forms and metaplectic forms
Read More ↓Edition Statements
- Publication Date:©2015
Publication Statements
- Publisher(s):American mathematical Society
- Place of Publication:Providence, Rhode Island
- Language:eng
- Publication Date:©2015
Notes
"Volume 237, number 1117 (first of 6 numbers), September 2015."
The Physical Object
- Description:1 online resource (v, 64 pages)
Edition Identifiers
- ISBN:9781470425012, 1470425017
- oclc:ocn917874773
- LC Classification:QA196
- Dewey Decimal:512.7
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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