Brandt Matrices and Theta Series over Global Function Fields

Brandt Matrices and Theta Series over Global Function Fields
Author :
Publisher : American Mathematical Soc.
Total Pages : 76
Release :
ISBN-10 : 9781470414191
ISBN-13 : 1470414198
Rating : 4/5 (91 Downloads)

Book Synopsis Brandt Matrices and Theta Series over Global Function Fields by : Chih-Yun Chuang

Download or read book Brandt Matrices and Theta Series over Global Function Fields written by Chih-Yun Chuang and published by American Mathematical Soc.. This book was released on 2015-08-21 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 ∞, 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.


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