Progress in Mathematics

MIATELLO R., WALLACH, NOLAN R.

M-series and Kloosterman-Selberg zeta functions for R-rank one groups

Birkhauser

Año: 2013;

Abstract. For an arbitrary Lie group G of real rank one, we give a formula for the Fourier coecient D 0 (;) of the M-series (a type of Poincar´e series) defined in [?], in terms of Kloosterman-Selberg zeta functions ;0; (). As a consequence we show that the meromorphic continuation of ;0; () to C follows from the meromorphic continuation of the M-series. We also give a description of the pole set in the region Re  0.