Brandt Matrices and Theta Series over Global Function Fields
Seiten
2015
American Mathematical Society (Verlag)
978-1-4704-1419-1 (ISBN)
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.
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 |
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