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Brandt Matrices and Theta Series over Global Function Fields

Chih-Yun Chuang
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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.
      Format: Paperback / softback CONTRIBUTORS: Chih-Yun Chuang EAN: 9781470414191 COUNTRY: United States PAGES: WEIGHT: 0 g HEIGHT: 254 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2015-09-01 CITY: GENRE: MATHEMATICS / Number Theory WIDTH: 178 cm SPINE:

      Book Themes:

      Number theory

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      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.
      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.
      Format: Paperback / softback CONTRIBUTORS: Chih-Yun Chuang EAN: 9781470414191 COUNTRY: United States PAGES: WEIGHT: 0 g HEIGHT: 254 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2015-09-01 CITY: GENRE: MATHEMATICS / Number Theory WIDTH: 178 cm SPINE:

      Book Themes:

      Number theory

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      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.

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