The hyperbolic circle problem over Heegner points
Number Theory
2025-06-18 v1
Abstract
For the full modular group, we obtain a logarithmic improvement on Selberg's long-standing bound for the error term of the counting function in the hyperbolic circle problem over Heegner points of different discriminants. The main ingredients in our method are Waldspurger's formula, twisted first moments of certain Rankin-Selberg convolutions, and a new fractional moment estimate.
Cite
@article{arxiv.2506.13883,
title = {The hyperbolic circle problem over Heegner points},
author = {Dimitrios Chatzakos and Giacomo Cherubini and Stephen Lester and Morten S. Risager},
journal= {arXiv preprint arXiv:2506.13883},
year = {2025}
}
Comments
35 pages