Brandt Matrices and Theta Series over Global Function Fields (eBook)

Chih-Yun Chuang (Autor)

eBook Download: PDF

2015
64 Seiten
American Mathematical Society (Verlag)
978-1-4704-2501-2 (ISBN)

Infos

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 "e;definite"e; 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 "e;compatibility"e; 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.

Produkt-Details

• Erscheint lt. Verlag: 8.8.2015
• Themenwelt: Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
• ISBN-10: 1-4704-2501-7 / 1470425017
• ISBN-13: 978-1-4704-2501-2 / 9781470425012