eBook ISBN:  9781470401795 
Product Code:  MEMO/124/594.E 
List Price:  $49.00 
MAA Member Price:  $44.10 
AMS Member Price:  $29.40 
eBook ISBN:  9781470401795 
Product Code:  MEMO/124/594.E 
List Price:  $49.00 
MAA Member Price:  $44.10 
AMS Member Price:  $29.40 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 124; 1996; 149 ppMSC: Primary 11; Secondary 22;
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.
ReadershipGraduate students and research mathematicians interested in number theory.

Table of Contents

Chapters

I. Introduction and statement of results

II. Evaluation of the integral for the main $H$relevant double cosets

III. Evaluation of the integrals for the other $H$relevant double cosets

IV. Evaluation of the $GSp(4)$ integral for the main double cosets

V. Evaluation of the $GSp(4)$ integrals for the other relevant double cosets


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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.
Graduate students and research mathematicians interested in number theory.

Chapters

I. Introduction and statement of results

II. Evaluation of the integral for the main $H$relevant double cosets

III. Evaluation of the integrals for the other $H$relevant double cosets

IV. Evaluation of the $GSp(4)$ integral for the main double cosets

V. Evaluation of the $GSp(4)$ integrals for the other relevant double cosets