Distribution of square integrable automorphic forms on Hilbert modular groups

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

Advanced Lecture in Math. Series 6, Analysis and Topology of Discrete Subgroups

International Press

Lugar: Boston; Año: 2008; p. 19 - 39

We apply the sum formula in [9] to obtain distribution results for cuspidal representations for Hilbert modular groups. The discrete subgroup is a Hecke type subgroup associated to  I, a non-zero ideal in the integers of the number field, and we allow a character  modulo I. In Section 3 (see Theorem 3.1 and consequences) we prove existence of cuspidal representations with specific components at some places ([8] and [9]). In the second part we give distribution results, as t tends \infty, for the number of cuspidal representations, weighted by Fourier coeffcients, that lie in suitable subregions At of the multieigenvalue space ([10]).We apply the sum formula in [9] to obtain distribution results for cuspidal representations for Hilbert modular groups. The discrete subgroup is a Hecke type subgroup associated to  I, a non-zero ideal in the integers of the number field, and we allow a character  modulo I. In Section 3 (see Theorem 3.1 and consequences) we prove existence of cuspidal representations with specific components at some places ([8] and [9]). In the second part we give distribution results, as t tends \infty, for the number of cuspidal representations, weighted by Fourier coeffcients, that lie in suitable subregions At of the multieigenvalue space ([10]).