Work

The hyperbolic circle problem over Heegner points

Year: 2025

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2506.13883

Authors: Chatzakos, Dimitrios, Cherubini, Giacomo, Lester, Stephen, Risager, Morten S.

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4415311097

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