Sum formula for SL_2 over a Totally Real Number Field

BRUGGEMAN, R. W., MIATELLO R.J.,

MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY (AMS)

AMER MATHEMATICAL SOC

Lugar: Providence; Año: 2009 vol. 197 p. 1 - 80

0065-9266

We state and prove a general form of the sum formulafor SL_2 over a totally real number field. This formula relatessums of Kloosterman sums to products of Fourier coefficients ofautomorphic representations. We give two versions: the spectralsum formula (in short: sum formula) and the Kloosterman sumformula, with the independent test function in the spectral term,respectively, the sum of Kloosterman sums. The discrete subgroup is Gamma_0(I), where I is a non-zero idealin the integers of the number field. We allow a character of theform mat  abcd mapsto ch(d), with ch$ a character modulo I