Brandt Matrices and Theta Series over Global Function Fields

Brandt Matrices and Theta Series over Global Function Fields

AngličtinaMäkká väzba
Chuang Chih-Yun
American Mathematical Society
EAN: 9781470414191
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Podrobné informácie

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.
EAN 9781470414191
ISBN 1470414198
Typ produktu Mäkká väzba
Vydavateľ American Mathematical Society
Dátum vydania 30. septembra 2015
Stránky 64
Jazyk English
Rozmery 254 x 178
Krajina United States
Autori Chuang Chih-Yun; Lee Ting-Fang; Wei Fu-Tsun; Yu Jing
Séria Memoirs of the American Mathematical Society