Electronic ISBN:  9781470405250 
Product Code:  MEMO/197/919.E 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 197; 2009; 81 ppMSC: Primary 11; 22;
The authors prove a general form of the sum formula \(\mathrm{SL}_2\) over a totally real number field. This formula relates sums of Kloosterman sums to products of Fourier coefficients of automorphic representations. The authors give two versions: the spectral sum formula (in short: sum formula) and the Kloosterman sum formula. They have the independent test function in the spectral term, in the sum of Kloosterman sums, respectively.

Table of Contents

Chapters

Introduction

Chapter 1. Spectral sum formula

Chapter 2. Kloosterman sum formula

Appendix A. Sum formula for the congruence subgroup $\Gamma _1(I)$

Appendix B. Comparisons


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The authors prove a general form of the sum formula \(\mathrm{SL}_2\) over a totally real number field. This formula relates sums of Kloosterman sums to products of Fourier coefficients of automorphic representations. The authors give two versions: the spectral sum formula (in short: sum formula) and the Kloosterman sum formula. They have the independent test function in the spectral term, in the sum of Kloosterman sums, respectively.

Chapters

Introduction

Chapter 1. Spectral sum formula

Chapter 2. Kloosterman sum formula

Appendix A. Sum formula for the congruence subgroup $\Gamma _1(I)$

Appendix B. Comparisons