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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)

Mathematical Theory

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In this paper we prove two equalities of local Kloosterman integrals on $\mathrm{GSp}\left(4\right)$, 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 $\mathrm{g1}\left(2\right)$ 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 $\mathrm{GSp}\left(4\right)$.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.

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Format: mass_market
ASIN: 0821833286
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Mathematical Theory
Domain: Amazon UK
Release Date: 31 July 2003
Listed Since: 10 December 2006

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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)

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