The fundamental lemma for the Bessel and Novodvorsky subgroups of GSp(4) II

Continuing from [2], we announce, in the case of the group GSp(4), another equality of two local integrals. One is a Kloosterman integral on the Besse l subgroups of GSp(4)(F) and the other is an iterated Kloosterman integral on the Novodvorsky subgroup and the subgroup GSp(4)(F) of GSp(4)(E), where F is a non-archimedean local field with the residual characteristic not equ al 2 and E is the unique unramified quadratic extension of F. We conjecture that Jacquet's relative trace formula for GL(2) in [6], where Jacquet has given another proof of Waldspurger's result [7], generalizes to GSp(4). Our result serves as the fundamental lemma for our conjectural relative trace formula for the main relevant double cosets. (C) 2000 Academie des sciences /Editions scientifiques et medicales Elsevier SAS.