Brandt Matrices and Theta Series over Global Function Fields

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

Format:Paperback

Publisher:American Mathematical Society

Published:30th Sep '15

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Brandt Matrices and Theta Series over Global Function Fields cover

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.

ISBN: 9781470414191

Dimensions: unknown

Weight: 130g

64 pages