On Central Critical Values Of The Degree Four L Functions For Gsp 4
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On Central Critical Values of the Degree Four $L$-Functions for GSp(4): The Fundamental Lemma. III
Author: Masaaki Furusawa
language: en
Publisher: American Mathematical Soc.
Release Date: 2013-08-23
Some time ago, the first and third authors proposed two relative trace formulas to prove generalizations of Böcherer's conjecture on the central critical values of the degree four -functions for , and proved the relevant fundamental lemmas. Recently, the first and second authors proposed an alternative third relative trace formula to approach the same problem and proved the relevant fundamental lemma. In this paper the authors extend the latter fundamental lemma and the first of the former fundamental lemmas to the full Hecke algebra. The fundamental lemma is an equality of two local relative orbital integrals. In order to show that they are equal, the authors compute them explicitly for certain bases of the Hecke algebra and deduce the matching.
On Central Critical Values of the Degree Four $L$-functions for $\mathrm {GSp}(4)$: The Fundamental Lemma
Author: Masaaki Furusawa
language: en
Publisher: American Mathematical Soc.
Release Date: 2003
Proves two equalities of local Kloosterman integrals on $\mathrm{GSp}\left(4\right)$, the group of $4$ by $4$ symplectic similitude matrices. This book conjectures 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}].
Transfer of Siegel Cusp Forms of Degree 2
Author: Ameya Pitale
language: en
Publisher: American Mathematical Soc.
Release Date: 2014-09-29
Let be the automorphic representation of generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and be an arbitrary cuspidal, automorphic representation of . Using Furusawa's integral representation for combined with a pullback formula involving the unitary group , the authors prove that the -functions are "nice". The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations have a functorial lifting to a cuspidal representation of . Combined with the exterior-square lifting of Kim, this also leads to a functorial lifting of to a cuspidal representation of . As an application, the authors obtain analytic properties of various -functions related to full level Siegel cusp forms. They also obtain special value results for and