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Brandt Matrices and Theta Series over Global Function Fields

Chih-Yun Chuang Taida Institute for Mathematical Sciences, Taipei, Taiwan
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
Available Formats:
Electronic ISBN: 978-1-4704-2501-2
Product Code: MEMO/237/1117.E
List Price: $68.00 MAA Member Price:$61.20
AMS Member Price: $40.80 Click above image for expanded view Brandt Matrices and Theta Series over Global Function Fields Chih-Yun Chuang Taida Institute for Mathematical Sciences, Taipei, Taiwan 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 Available Formats:  Electronic ISBN: 978-1-4704-2501-2 Product Code: MEMO/237/1117.E  List Price:$68.00 MAA Member Price: $61.20 AMS Member Price:$40.80
• Book Details

Memoirs of the American Mathematical Society
Volume: 2372015; 64 pp
MSC: Primary 11;

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.

• Chapters
• 1. Introduction
• 2. Brandt matrices and definite Shimura curves
• 3. The basis problem for Drinfeld type automorphic forms
• 4. Metaplectic forms and Shintani-type correspondence
• 5. Trace formula of Brandt matrices
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Volume: 2372015; 64 pp
MSC: Primary 11;

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.

• Chapters
• 1. Introduction
• 2. Brandt matrices and definite Shimura curves
• 3. The basis problem for Drinfeld type automorphic forms
• 4. Metaplectic forms and Shintani-type correspondence
• 5. Trace formula of Brandt matrices
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
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