On Central Critical Values of the Degree Four L-functions for Gsp4: The Fundamental Lemma - Couverture souple

American Mathematical Society

Couverture souple

ISBN 10 : 0821833286 ISBN 13 : 9780821833285

Editeur : American Mathematical Society, 2003

Synopsis

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.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2003
• Langue: anglais
• ISBN 10: 0821833286
• ISBN 13: 9780821833285
• Reliure: Poche
• Nombre de pages: 139
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible