04170nam 2200613 450 991081240700332120170822102510.01-4704-0179-7(CKB)3360000000464778(EBL)3113802(SSID)ssj0000888943(PQKBManifestationID)11453157(PQKBTitleCode)TC0000888943(PQKBWorkID)10867697(PQKB)11652887(MiAaPQ)EBC3113802(RPAM)1635791(PPN)195414764(EXLCZ)99336000000046477820140903h19961996 uy 0engur|n|---|||||txtccrThe fundamental lemma of the Shalika subgroup of GL(4) /Solomon Friedberg, Hervé JacquetProvidence, Rhode Island :American Mathematical Society,1996.©19961 online resource (167 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 124, Number 594"November 1996, Volume 124, Number 594 (end of volume)."0-8218-0540-1 Includes bibliographical references.""Contents""; ""Chapter I. Introduction and Statement of Results""; ""1. Introduction""; ""2. The Shalika Subgroup H of GL(4): Relevant Double Cosets and Kloosterman Integrals""; ""3. The Symplectic Group GS[sub(p)](4): Relevant Double Cosets and Kloosterman Integrals""; ""4. The Main Theorem""; ""5. Kloosterman Integrals and Gauss Sums""; ""Chapter II. Evaluation of the Integral for the Main H-Relevant Double Cosets""; ""1. Plan of the Computation""; ""2. The Unipotent Integral""; ""3. The Toroidal Integral""; ""4. Two Supplementary Integrals""""5. Evaluation of the Mellin Transform I: The Ramified Case""""6. Evaluation of the Mellin Transform II: The Case Ï?[sub(1)]Ramified, Ï?[sub(2)] Unramified""; ""7. Evaluation of the Mellin Transform III: The Case Ï?[sub(1)]Unramified, Ï?[sub(2)]Ramified""; ""8. Evaluation of the Mellin Transform IV: The Unramified Case""; ""Chapter III. Evaluation of the Integrals for the Other if-Relevant Double Cosets""; ""1. Evaluation of the Integral M[sub(F)](Ï?[sub(1); 1), I: Unipotent Integration""; ""2. Evaluation of the Integral M[sub(F)](Ï?[sub(1); 1), II: Toroidal Integration and Simplification""""3. Evaluation of the Integral M[sub(F)](Ï?[sub(1)132), I: Unipotent Integration""; ""4. Evaluation of the Integral M[sub(F)](Ï?[sub(1); 132), II: Toroidal Integration and Simplification""; ""Chapter IV. Evaluation of the GS[sub(p)](4) Integral for the Main Double Cosets""; ""1. Computation of the Integral J(t)""; ""2. Simplification of the Integrals Giving J(t)""; ""3. Computation of the Mellin Transform""; ""4. Evaluation of the Mellin Transform I: The Ramified Case""; ""5. Evaluation of the Mellin Transform II: The Case Ï?[sub(1)] Ramified, Ï?[sub(2)] Unramified""""6. Evaluation of the Mellin Transform III: The Case Ï?[sub(1)] Unramified, Ï?[sub(2)] Ramified""""7. Evaluation of the Mellin Transform IV: The Unramified Case""; ""Chapter V. Evaluation of the G5[sub(p)](4) Integrals for the Other Relevant Double Cosets""; ""1. Computation of the Integral J(Ï?[sub(1)],t)""; ""2. Evaluation of the Mellin Transform M[sub(J)](Ï?Ï?[sub(1)])""; ""3. Computation of the Integral J(Ï?[sub(2)],t)""; ""4. Evaluation of the Mellin Transform M[sub(J)](Ï?Ï?[sub(1)])""; ""References""Memoirs of the American Mathematical Society ;Volume 124, Number 594.Automorphic formsTrace formulasRepresentations of groupsAutomorphic forms.Trace formulas.Representations of groups.512/.7Friedberg Solomon1958-1614301Jacquet Hervé1939-MiAaPQMiAaPQMiAaPQBOOK9910812407003321The fundamental lemma of the Shalika subgroup of GL(4)4082143UNINA