000			04139nam a22004933i 4500
001			EBC5295323
003			MiAaPQ
005			20240729131757.0
006			m o d |
007			cr cnu||||||||
008			240724s2014 xx o ||||0 eng d
020			_a9781470418939 _q(electronic bk.)
020			_z9780821898567
035			_a(MiAaPQ)EBC5295323
035			_a(Au-PeEL)EBL5295323
035			_a(OCoLC)890463876
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA243 .P58 2014
082	0		_a512.7
100	1		_aPitale, Ameya.
245	1	0	_aTransfer of Siegel Cusp Forms of Degree 2.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2014.
264		4	_c©2014.
300			_a1 online resource (120 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society Series ; _vv.232
505	0		_aCover -- Title page -- Introduction -- Notation -- Chapter 1. Distinguished vectors in local representations -- 1.1. Parabolic induction to (2,2) -- 1.2. Distinguished vectors: non-archimedean case -- 1.3. Distinguished vectors: archimedean case -- 1.4. Intertwining operator: non-archimedean case -- 1.5. Intertwining operator: archimedean case -- Chapter 2. Global -functions for ₄× ₂ -- 2.1. Bessel models for ₄ -- 2.2. Local zeta integrals -- 2.3. The global integral representation -- 2.4. The functional equation -- Chapter 3. The pullback formula -- 3.1. Local sections: non-archimedean case -- 3.2. The local pullback formula: non-archimedean case -- 3.3. Local sections: archimedean case -- 3.4. The local pullback formula: archimedean case -- 3.5. The global pullback formula -- 3.6. The second global integral representation -- Chapter 4. Holomorphy of global -functions for ₄× ₂ -- 4.1. Preliminary considerations -- 4.2. Eisenstein series and Weil representations -- 4.3. The Siegel-Weil formula and the proof of entireness -- Chapter 5. Applications -- 5.1. The transfer theorems -- 5.2. Analytic properties of -functions -- 5.3. Critical values of -functions -- Bibliography -- Back Cover.
520			_aLet \pi be the automorphic representation of \textrm{GSp}_4(\mathbb{A}) generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and \tau be an arbitrary cuspidal, automorphic representation of \textrm{GL}_2(\mathbb{A}). Using Furusawa's integral representation for \textrm{GSp}_4\times\textrm{GL}_2 combined with a pullback formula involving the unitary group \textrm{GU}(3,3), the authors prove that the L-functions L(s,\pi\times\tau) are "nice". The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations \pi have a functorial lifting to a cuspidal representation of \textrm{GL}_4(\mathbb{A}). Combined with the exterior-square lifting of Kim, this also leads to a functorial lifting of \pi to a cuspidal representation of \textrm{GL}_5(\mathbb{A}). As an application, the authors obtain analytic properties of various L-functions related to full level Siegel cusp forms. They also obtain special value results for \textrm{GSp}_4\times\textrm{GL}_1 and \textrm{GSp}_4\times\textrm{GL}_2.
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	_aCusp forms (Mathematics).
650		0	_aSiegel domains.
650		0	_aModular groups.
655		4	_aElectronic books.
700	1		_aSaha, Abhishek.
700	1		_aSchmidt, Ralf.
776	0	8	_iPrint version: _aPitale, Ameya _tTransfer of Siegel Cusp Forms of Degree 2 _dProvidence : American Mathematical Society,c2014 _z9780821898567
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society Series
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5295323 _zClick to View
999			_c136279 _d136279