ISBN: 9780821833285
ID: 6416318
In this paper we prove two equalities of local Kloosterman integrals on $mathrm{GSp}left(4; ight)$, the group of $4$ by $4$ symplectic similitude matrices. One is an equality between the Novodvorsky orbital integral and the Bessel orbital integral and the other one is an equality between the Bessel orbital integral and the quadratic orbital integral. We conjecture that both of Jacquet's relative In this paper we prove two equalities of local Kloosterman integrals on $mathrm{GSp}left(4; ight)$, the group of $4$ by $4$ symplectic similitude matrices. One is an equality between the Novodvorsky orbital integral and the Bessel orbital integral and the other one is an equality between the Bessel orbital integral and the quadratic orbital integral. We conjecture that both of Jacquet's relative trace formulas for the central critical values of the $L$-functions for $mathrm{g1}left(2; ight)$ in [{J1}] and [{J2}], where Jacquet has given another proof of Waldspurger's result [{W2}], generalize to the ones for the central critical values of the degree four spinor $L$-functions for $mathrm{GSp}left(4; ight)$.We believe that our approach will lead us to a proof and also a precise formulation of a conjecture of Bocherer [{B}] and its generalization. Support for this conjecture may be found in the important paper of Bocherer and Schulze-Pillot [{BSP}]. Also a numerical evidence has been recently given by Kohnen and Kuss [{KK}]. Our results serve as the fundamental lemmas for our conjectural relative trace formulas for the main relevant double cosets. Books, Science and Geography~~Mathematics~~Number Theory, On Central Critical Values Of The Degree Four L-Functions For Gsp(4)~~Book~~9780821833285~~Masaaki Furusawa, Joseph A. Shalika, , , , , , , , , ,, [PU: American Mathematical Society]
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On Central Critical Values of the Degree Four L-functions for GSp(4): The Fundamental Lemma (Memoirs of the American Mathematical Society) - PaperbackISBN: 0821833286
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On Central Critical Values of the Degree Four L-Functions for GSp(4): The Fundamental Lemma (Memoirs of the American Mathematical Society) - Paperback
ISBN: 0821833286
Taschenbuch, [EAN: 9780821833285], American Mathematical Society, American Mathematical Society, Book, [PU: American Mathematical Society], American Mathematical Society, 56247011, Zahlentheorie, 56230011, Reine Mathematik, 56214011, Mathematik, 56047011, Fachbücher, 54071011, Genres, 52044011, Fremdsprachige Bücher, 208623031, Taschenbuch, 208621031, Format (binding_browse-bin), 366250011, Refinements, 52044011, Fremdsprachige Bücher
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Title: | On Central Critical Values of the Degree Four L-Functions for GSp(4): The Fundamental Lemma (Memoirs of the American Mathematical Society) |
ISBN: | 0821833286 |
Details of the book - On Central Critical Values of the Degree Four L-Functions for GSp(4): The Fundamental Lemma (Memoirs of the American Mathematical Society)
EAN (ISBN-13): 9780821833285
ISBN (ISBN-10): 0821833286
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ISBN/EAN: 0821833286
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