arXiv subjects

R. W. Bruggeman

Publications and source records attributed to R. W. Bruggeman.

3 recordsLinked to original sources

arXiv2009

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 $F$, with discrete subgroup of Hecke type $Γ_0(I)$ for a non-zero ideal $I$ in the ring of integers of $F$. 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 $F$. The main tool in the derivation is a sum formula of Kuznetsov type.

math.NT↗

arXiv2007

Eigenfunctions of transfer operators and cohomology

The eigenfunctions with eigenvalues 1 or -1 of the transfer operator of Mayer are in bijective correspondence with the eigenfunctions with eigenvalue 1 of a transfer operator connected to the nearest integer continued fraction algorithm. This is shown by relating these eigenspaces of these operators to cohomology groups for the modular group with coefficients in certain principal series representations.

math.NT↗

arXiv2002

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.

math.NT↗