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Sum Formula for SL$$_2$$ over a Totally Real Number Field
Roelof W. Bruggeman, Universiteit Utrecht, The Netherlands, and Roberto J. Miatello, Universidad Nacional de Córdoba, Argentina
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Memoirs of the American Mathematical Society
2009; 81 pp; softcover
Volume: 197
ISBN-10: 0-8218-4202-1
ISBN-13: 978-0-8218-4202-7
List Price: US$62 Individual Members: US$37.20
Institutional Members: US\$49.60
Order Code: MEMO/197/919

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.

• Appendix A. Sum formula for the congruence subgroup $$\Gamma_{1}(I)$$