arXiv subjects

Svenja zur Verth

Publications and source records attributed to Svenja zur Verth.

2 recordsLinked to original sources

arXiv2026

Non-vanishing of central values of L-functions with angular restrictions

We study the angular restrictions for the second moment of toroidal families of $L$-functions using the general theory of trace functions. With the mollification technique we deduce non-vanishing of a positive proportion. Our two main ingredients are classification results of Katz to determine the sheaves at play and a recent result of Fouvry, Kowalski, Michel and Sawin to bound bilinear sums of their trace functions.

math.NT↗

arXiv2025

Solving quadratic forms in restricted variables with the circle method

Let $f(\mathbf x)$ be a non-singular quadratic form with sufficiently many mixed terms and $t$ an integer. For a sequence of weights $\mathcal A$ we study the number of weighted solutions to $f(\mathbf x) = t$. In particular, we give conditions on both $\mathcal A$ and $f$ such that we can use the circle method to count such solutions of bounded height.

math.NT↗