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Brandt matrices and theta series over global function fields / Chih-Yun Chuang...[et al.].

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v 237, no 1117.Publication details: Providence : American Mathematical Society, 2015.Description: v, 64 p. ; 26 cmISBN:
  • 9781470414191 (pbk. : alk. paper)
Subject(s): DDC classification:
  • 510 23 Am512
Contents:
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 -- Bibliography.
Summary: 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.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 510 Am512 (Browse shelf(Opens below)) Available 136674
Total holds: 0

Includes bibliographical references.

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 --
Bibliography.

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.

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