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The Fundamental Lemma for the Shalika Subgroup of $GL(4)$
 
Solomon Friedberg University of California Santa Cruz
Hervé Jacquet Columbia University
The Fundamental Lemma for the Shalika Subgroup of $GL(4)$
eBook ISBN:  978-1-4704-0179-5
Product Code:  MEMO/124/594.E
List Price: $49.00
MAA Member Price: $44.10
AMS Member Price: $29.40
The Fundamental Lemma for the Shalika Subgroup of $GL(4)$
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The Fundamental Lemma for the Shalika Subgroup of $GL(4)$
Solomon Friedberg University of California Santa Cruz
Hervé Jacquet Columbia University
eBook ISBN:  978-1-4704-0179-5
Product Code:  MEMO/124/594.E
List Price: $49.00
MAA Member Price: $44.10
AMS Member Price: $29.40
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1241996; 149 pp
    MSC: 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 L-function heuristics which motivate this work, its possible generalizations, and an application of the relative trace formula to the study of L-packets.

    Readership

    Graduate 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1241996; 149 pp
MSC: 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 L-function heuristics which motivate this work, its possible generalizations, and an application of the relative trace formula to the study of L-packets.

Readership

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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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