eBook ISBN:  9781470410575 
Product Code:  MEMO/225/1057.E 
List Price:  $74.00 
MAA Member Price:  $66.60 
AMS Member Price:  $44.40 
eBook ISBN:  9781470410575 
Product Code:  MEMO/225/1057.E 
List Price:  $74.00 
MAA Member Price:  $66.60 
AMS Member Price:  $44.40 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 225; 2013; 134 ppMSC: Primary 11
Some time ago, the first and third authors proposed two relative trace formulas to prove generalizations of Böcherer's conjecture on the central critical values of the degree four \(L\)functions for \(\mathrm{GSp}(4)\), and proved the relevant fundamental lemmas. Recently, the first and second authors proposed an alternative third relative trace formula to approach the same problem and proved the relevant fundamental lemma. In this paper the authors extend the latter fundamental lemma and the first of the former fundamental lemmas to the full Hecke algebra. The fundamental lemma is an equality of two local relative orbital integrals. In order to show that they are equal, the authors compute them explicitly for certain bases of the Hecke algebra and deduce the matching.

Table of Contents

Chapters

Preface

1. Introduction

2. Reduction Formulas

3. Anisotropic Bessel Orbital Integral

4. Split Bessel and Novodvorsky Orbital Integrals

5. RankinSelberg Orbital Integral


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Some time ago, the first and third authors proposed two relative trace formulas to prove generalizations of Böcherer's conjecture on the central critical values of the degree four \(L\)functions for \(\mathrm{GSp}(4)\), and proved the relevant fundamental lemmas. Recently, the first and second authors proposed an alternative third relative trace formula to approach the same problem and proved the relevant fundamental lemma. In this paper the authors extend the latter fundamental lemma and the first of the former fundamental lemmas to the full Hecke algebra. The fundamental lemma is an equality of two local relative orbital integrals. In order to show that they are equal, the authors compute them explicitly for certain bases of the Hecke algebra and deduce the matching.

Chapters

Preface

1. Introduction

2. Reduction Formulas

3. Anisotropic Bessel Orbital Integral

4. Split Bessel and Novodvorsky Orbital Integrals

5. RankinSelberg Orbital Integral