The authors establish the fundamental lemma for a relative trace formula. This fundamental 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 L-function heuristics which motivate this work, its possible generalizations, and an application of the relative trace formula to the study of L-packets.
- ISBN13 9780821805404
- Publish Date 1 January 1996
- Publish Status Active
- Publish Country US
- Imprint American Mathematical Society
- Format Paperback
- Pages 149
- Language English