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005			20240729131156.0
006			m o d |
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008			240724s2015 xx o ||||0 eng d
020			_a9781470425012 _q(electronic bk.)
020			_z9781470414191
035			_a(MiAaPQ)EBC4832024
035			_a(Au-PeEL)EBL4832024
035			_a(CaPaEBR)ebr11367309
035			_a(OCoLC)917874773
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA196.B736 2015
082	0		_a512.70000000000005
100	1		_aChuang, Chih-Yun.
245	1	0	_aBrandt Matrices and Theta Series over Global Function Fields.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2015.
264		4	_c©2015.
300			_a1 online resource (76 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society ; _vv.237
505	0		_aCover -- Title page -- Chapter 1. Introduction -- Chapter 2. Brandt matrices and definite Shimura curves -- 1. Basic setting -- 2. Definite quaternion algebra over function fields -- 3. Brandt matrices -- 4. Definite Shimura curves -- 4.1. Hecke correspondences -- 4.2. Gross height pairing -- Chapter 3. The basis problem for Drinfeld type automorphic forms -- 1. Weil representation -- 1.1. Weil representation of \SL₂× ( ) -- 1.2. Test functions from arithmetic data -- 2. Theta series -- 3. Drinfeld type automorphic forms and Hecke operators -- 3.1. Fourier coefficients of theta series -- 4. The Hecke module homomorphism Φ -- 4.1. Changing levels -- 5. Construction of Drinfeld type newforms -- 6. The basis problem -- Chapter 4. Metaplectic forms and Shintani-type correspondence -- 1. Metaplectic forms -- 1.1. Metaplectic group -- 1.2. Weil representation and theta series from pure quaternions -- 1.3. Fourier coefficients of metaplectic theta series -- 2. Hecke operators and Shintani-type correspondence -- 3. Pure quaternions and Brandt matrices -- Chapter 5. Trace formula of Brandt matrices -- 1. Optimal embeddings -- 1.1. Local optimal embeddings -- 2. Trace formula -- Bibliography -- Symbols -- Back Cover.
520			_aThe 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.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aMatrices.
655		4	_aElectronic books.
700	1		_aLee, Ting-Fang.
700	1		_aWei, Fu-Tsun.
700	1		_aYu, Jing.
776	0	8	_iPrint version: _aChuang, Chih-Yun _tBrandt Matrices and Theta Series over Global Function Fields _dProvidence : American Mathematical Society,c2015 _z9781470414191
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4832024 _zClick to View
999			_c124845 _d124845