The hyperbolic circle problem over Heegner points

Fuente: arXiv
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Main Authors: Chatzakos, Dimitrios, Cherubini, Giacomo, Lester, Stephen, Risager, Morten S.
Format: Preprint
Published: 2025
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author Chatzakos, Dimitrios
Cherubini, Giacomo
Lester, Stephen
Risager, Morten S.
author_facet Chatzakos, Dimitrios
Cherubini, Giacomo
Lester, Stephen
Risager, Morten S.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2506_13883
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The hyperbolic circle problem over Heegner points
Chatzakos, Dimitrios
Cherubini, Giacomo
Lester, Stephen
Risager, Morten S.
Number Theory
11P21 11N45 11F67,
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.
title The hyperbolic circle problem over Heegner points
topic Number Theory
11P21 11N45 11F67,
url https://arxiv.org/abs/2506.13883