TY  - BOOK
AU  - Chuang,Chih-Yun
AU  - Lee,Ting-Fang
AU  - Wei,Fu-Tsun
AU  - Yu,Jing
TI  - Brandt Matrices and Theta Series over Global Function Fields
T2  - Memoirs of the American Mathematical Society
SN  - 9781470425012
AV  - QA196.B736 2015 
U1  - 512.70000000000005 
PY  - 2015///
CY  - Providence
PB  - American Mathematical Society
KW  - Matrices
KW  - Electronic books
N1  - Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Brandt matrices and definite Shimura curves -- 1. Basic setting -- 2. Definite quaternion algebra over function fields -- 3. Brandt matrices -- 4. Definite Shimura curves -- 4.1. Hecke correspondences -- 4.2. Gross height pairing -- Chapter 3. The basis problem for Drinfeld type automorphic forms -- 1. Weil representation -- 1.1. Weil representation of \SL₂× ( ) -- 1.2. Test functions from arithmetic data -- 2. Theta series -- 3. Drinfeld type automorphic forms and Hecke operators -- 3.1. Fourier coefficients of theta series -- 4. The Hecke module homomorphism Φ -- 4.1. Changing levels -- 5. Construction of Drinfeld type newforms -- 6. The basis problem -- Chapter 4. Metaplectic forms and Shintani-type correspondence -- 1. Metaplectic forms -- 1.1. Metaplectic group -- 1.2. Weil representation and theta series from pure quaternions -- 1.3. Fourier coefficients of metaplectic theta series -- 2. Hecke operators and Shintani-type correspondence -- 3. Pure quaternions and Brandt matrices -- Chapter 5. Trace formula of Brandt matrices -- 1. Optimal embeddings -- 1.1. Local optimal embeddings -- 2. Trace formula -- Bibliography -- Symbols -- Back Cover
N2  - 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
UR  - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4832024
ER  -