Brandt Matrices and Theta Series over Global Function Fields - Couverture souple

Chuang, Chih-Yun; Lee, Ting-Fang; Wei, Fu-Tsun; Yu, Jing

Couverture souple

ISBN 10 : 1470414198 ISBN 13 : 9781470414191

Editeur : American Mathematical Society, 2015

Synopsis

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.

A propos du livre

À propos de l?auteur

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.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2015
• Langue: anglais
• ISBN 10: 1470414198
• ISBN 13: 9781470414191
• Reliure: Broché
• Nombre de pages: 64
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible