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Sum Formula for SL$_2$ over a Totally Real Number Field

Roelof W. Bruggeman Universiteit Utrecht, Utrecht, The Netherlands
Roberto J. Miatello Universidad Nacional de Córdoba, Córdoba, Argentina
Available Formats:
Electronic ISBN: 978-1-4704-0525-0
Product Code: MEMO/197/919.E
List Price: $66.00 MAA Member Price:$59.40
AMS Member Price: $39.60 Click above image for expanded view Sum Formula for SL$_2$over a Totally Real Number Field Roelof W. Bruggeman Universiteit Utrecht, Utrecht, The Netherlands Roberto J. Miatello Universidad Nacional de Córdoba, Córdoba, Argentina Available Formats:  Electronic ISBN: 978-1-4704-0525-0 Product Code: MEMO/197/919.E  List Price:$66.00 MAA Member Price: $59.40 AMS Member Price:$39.60
• Book Details

Memoirs of the American Mathematical Society
Volume: 1972009; 81 pp
MSC: 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.

• 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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Volume: 1972009; 81 pp
MSC: 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.

• 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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