Hervé Jacquet

D. Goldfeld

Herve Jacquet is one of the founders of the modern theory of automorphic representations and their associated $L$-functions. This volume represents a selection of his most influential papers not already available in book form. The volume contains papers on the $L$-function attached to a pair of representations of the general linear group. Thus, it completes Jacquet's papers on the subject (joint with Shalika and Piatetski-Shapiro) that can be found in the volume of selected works of Piatetski-Shapiro. In particular, two often quoted papers of Jacquet and Shalika on the classification of automorphic representations and a historically important paper of Gelbart and Jacquet on the functorial transfer from $GL(2)$ to $GL(3)$ are included. Another series of papers pertains to the relative trace formula introduced by Jacquet. This is a variant of the standard trace formula which is used to study the period integrals of automorphic forms. Nearly complete results are obtained for the period of an automorphic form over a unitary group.

Collected Works of Herve Jacquet

Solomon Friedberg

The authors establish the fundamental lemma for a relative trace formula. The trace formula compares generic automorphic representations of [italic capitals]GS[italic]p(4) with automorphic representations of [italic capitals]GS(4) which are distinguished with respect to a character of the Shalika subgroup, the subgroup of matrices of 2 x 2 block form ([superscript italic]g [over] [subscript capital italic]X [and] 0 [over] [superscript italic]g). The fundamental lemma, giving the equality of the orbital integrals of the unit elements of the respective Hecke algebras, amounts to a comparison of certain exponential sums arising from these two different groups.

Hervé Jacquet

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