Memoirs of the American Mathematical Society 2013; 134 pp; softcover Volume: 225 ISBN10: 0821887424 ISBN13: 9780821887424 List Price: US$74 Individual Members: US$44.40 Institutional Members: US$59.20 Order Code: MEMO/225/1057
 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 \(L\)functions for \(\mathrm{GSp}(4)\), 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. Table of Contents  Introduction
 Reduction formulas
 Anisotropic Bessel orbital integral
 Split Bessel and Novodvorsky orbital integrals
 RankinSelberg orbital integral
 Bibliography
 Index
