arXiv subjects

Werner Müller

Publications and source records attributed to Werner Müller.

2 recordsLinked to original sources

arXiv2026

On the absolute convergence of the spectral side of the twisted trace formula

We establish the absolute convergence of the spectral side of the twisted trace formula for reductive algebraic groups. More precisely, we extend the absolute convergence theorem of the spectral side due to Finis--Lapid--M\"uller to the twisted setting. This paper provides a detailed proof of the absolute convergence theorem, whose proof is known to experts but does not seem to have appeared in the literature. The resulting formulas are motivated by applications to limit multiplicity problems and to Weyl laws for self-dual automorphic representations of $\mathrm{GL}_n$.

math.RT↗

arXiv2012

Spectral theory for the Weil-Petersson Laplacian on the Riemann moduli space

We study the spectral geometric properties of the scalar Laplace-Beltrami operator associated to the Weil-Petersson metric $g_{\mathrm{WP}}$ on $\mathcal M_γ$, the Riemann moduli space of surfaces of genus $γ> 1$. This space has a singular compactification with respect to $g_{\mathrm{WP}}$, and this metric has crossing cusp-edge singularities along a finite collection of simple normal crossing divisors. We prove first that the scalar Laplacian is essentially self-adjoint, which then implies that its spectrum is discrete. The second theorem is a Weyl asymptotic formula for the counting function for this spectrum.

math.DG↗