TY - BOOK AU - Furusawa,Masaaki AU - Martin,Kimball AU - Shalika,Joseph A. TI - On central critical values of the degree four L-functions for GSp(4): the fundamental lemma T2 - Memoirs of the American Mathematical Society, SN - 0821887424 U1 - 510 PY - 2013/// CY - Providence, Rhode Island PB - American Mathematical Society KW - Siegel domains KW - Modular groups KW - Automorphic forms N1 - "Volume 225, number 1057 (second of 4 numbers), September 2013."; The first volume of "On central critical values of the degree four L-functions for GSp(4)" was published as number 782 of the Memoirs of the American Mathematical Society in 2003; the second volume was published in volume 133 of the American Journal of Mathematics in 2011; Includes bibliographical references (p. 131-132) and index; Introduction: Notation. Orbital Integrals ; Matching -- Reduction formulas. Macdonald Polynomials ; Explicit formulas and the Macdonald Polynomials ; Reduction formulas for the orbital integrals -- Anisotropic Bessel Orbital Integral. Preliminaries ; Evaluation -- Split Bessel and Novodvorsky Orbital Integrals. Preliminaries ; Evaluation ; Matching -- Rankin-Selberg Orbital Integral. Preliminaries ; Matching in the inert case ; Matching in the split case ER -