Memoirs of the American Mathematical Society 1996; 149 pp; softcover Volume: 124 ISBN10: 0821805401 ISBN13: 9780821805404 List Price: US$49 Individual Members: US$29.40 Institutional Members: US$39.20 Order Code: MEMO/124/594
 The authors establish the fundamental lemma for a relative trace formula. This fundmental lemma asserts that pairs of local orbital integrals, one integral of each pair arising on \(GSp(4)\) and the other on \(GL(4)\), are equal. The orbital integrals in question are exponential sums, and the fundamental lemma may also be described as a matching of Kloosterman and relative Kloosterman sums on the two different groups. To show that these are equal for each relevant Weyl groups element, the authors compute the Mellin transforms and match them in all cases. The authors also describe the Lfunction heuristics which motivate this work, its possible generalizations, and an application of the relative trace formula to the study of Lpackets. Readership Graduate students and research mathematicians interested in number theory. Table of Contents  Introduction and statement of results
 Evaluation of the integral for the main \(H\)relevant double cosets
 Evaluation of the integrals for the other \(H\)relevant double cosets
 Evaluation of the \(GSp(4)\) integral for the main double cosets
 Evaluation of the \(GSp(4)\) integrals for the other relevant double cosets
 References
