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Density results for automorphic forms on Hilbert modular groups
We give density results for automorphic representations of Hilbert modular
groups. In particular, we show that there are infinitely many automorphic
representations that have a prescribed discrete series factor at some (but not
all) real places.Comment: 35 pages, LaTe
Density results for automorphic forms on Hilbert modular groups II
We obtain an asymptotic formula for a weighted sum over cuspidal eigenvalues
in a specific region, for \SL_2 over a totally real number field , with
discrete subgroup of Hecke type for a non-zero ideal in the
ring of integers of . The weights are products of Fourier coefficients. This
implies in particular the existence of infinitely many cuspidal automorphic
representations with multi-eigenvalues in various regions growing to infinity.
For instance, in the quadratic case, the regions include floating boxes,
floating balls, sectors, slanted strips and products of prescribed small
intervals for all but one of the infinite places of . The main tool in the
derivation is a sum formula of Kuznetsov type.Comment: Accepted for publication by the Transactions of the American
Mathematical Societ
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