Brandt Matrices and Theta Series Over Global Function Fields

Chih-Yun Chuang, Ting-Fang Lee, Fu-Tsun Wei, Jing Yu (Autoren)

Buch | Softcover

64 Seiten

2015
American Mathematical Society (Verlag)
978-1-4704-1419-1 (ISBN)

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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.

Chih-Yun Chuang and Ting-Fang Lee, Taida Institute for Mathematical Sciences, Taipei, Taiwan. Fu-Tsun Wei, Institute of Mathematics, Academia Sinica, Taipei, Taiwan. Jing Yu, National Taiwan University, Taipei, Taiwan.

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

Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	130 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
ISBN-10	1-4704-1419-8 / 1470414198
ISBN-13	978-1-4704-1419-1 / 9781470414191
Zustand	Neuware