Leonhard Hochfilzer

Mathematician


My Interests:

I am mainly focussing on problems dealing with the quantitative arithmetic of varieties. In simple terms: I want to understand the number of rational solutions of bounded height to a set of polynomial equations asymptotically as the height grows toward infinity. In the past I have been particularly interested in such problems over function fields and number fields.

In the past I have done some research on Artin L-functions and Maass forms joint with Thomas Oliver. During my Master's project I investigated von Mangoldt functions attached to Galois representations of function fields, and how random matrix theory can help us to understand them in short intervals (article below). Here is an accessible summary about this project.

On the side I have also been involved in some applied projects.

Publications & Pre-prints: