arXiv subjects

Gilles Felber

Publications and source records attributed to Gilles Felber.

4 recordsLinked to original sources

arXiv2026

Counting Representations of Quadratic Forms

We answer a question of C. S. Herz about the number of integral $k\times m$ matrices $T$ such that $T^tT\leq R$ for a fixed positive definite $m\times m$ matrix $R$. We give an asymptotic formula for the count. This can be seen as a generalization of the Gauss circle problem, as counting representation of quadratic forms by the identity $I_k$, and as counting integral points bounded by the Stiefel manifold $T^tT=R$. The main tool is a bound for Bessel functions of matrix argument that was proved over Jordan algebras.

math.NT↗

arXiv2026

Bounds on Whittaker Functions for $\mathrm{GL}(n)$

We prove a new estimate on Jacquet-Whittaker function for $\mathrm{GL}_n(\mathbb R)$, assuming that the Langlands parameters are purely imaginary and well-spaced. This gives an upper bound for the global sup-norm of the Whittaker function that matches the lower bound of Brumley-Templier in the exponent up to a linear error in $n$.

math.NT↗

arXiv2025

Symplectic Kloosterman Sums for $\operatorname{Sp}(2n)$ with Powerful Moduli

We prove a non-trivial bound for $\operatorname{Sp}(2n)$ Kloosterman sums of moduli not equal to a prime multiple of the identity. These sums are attached to Siegel modular forms on the group $\operatorname{Sp}(2n)$ and appear in the corresponding Petersson formula. We give an application to equidistribution of coprime symmetric pairs.

math.NT↗

arXiv2023

A Restriction Norm Problem for Siegel Modular Forms

We establish an asymptotic formula with a power-saving error of the $L^2$-norm of Siegel cusp forms of degree 2 in an average sense when restricted to the imaginary axis. The result is consistent with the Mass Equidistribution Conjecture for Siegel modular forms and the Lindelöf Hypothesis for some twisted Koecher-Maass series. Along the way, we perform a careful analysis of the Kitaoka formula of degree 2.

math.NT↗