| Description |
1 online resource (v, 64 pages) |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; volume 237, number 1117 |
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Memoirs of the American Mathematical Society ; no. 1117.
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| Contents |
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 |
| 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 [infinity symbol], we 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 our theta series, and thereby contributes to the so-called basis problem. Restricting the norm forms to pure quaternions, we obtain another family of theta series which are automorphic functions on the metaplectic group, and results in a Shintani-type correspondence between Drinfeld type forms and metaplectic forms |
| Bibliography |
Includes bibliographical references (page 61) |
| Notes |
"Volume 237, number 1117 (first of 6 numbers), September 2015." |
|
Online resource; title from PDF title page (viewed October 6, 2015) |
| Subject |
Matrices.
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Quaternions.
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Hecke algebras.
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Series, Theta.
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Hecke algebras
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Matrices
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Quaternions
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Series, Theta
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| Form |
Electronic book
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| Author |
Lee, Ting-Fang, 1981- author.
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Wei, Fu-Tsun, 1981- author.
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Yu, Jing, 1949- author.
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American Mathematical Society, publisher
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| ISBN |
9781470425012 |
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1470425017 |
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