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arXiv · 2506.13883

The hyperbolic circle problem over Heegner points

Dimitrios Chatzakos·Giacomo Cherubini·Stephen Lester·Morten S. Risager
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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.

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Dimitrios Chatzakos, Giacomo Cherubini, Stephen Lester, Morten S. Risager. 2025-06-16. The hyperbolic circle problem over Heegner points. https://arxiv.org/abs/2506.13883

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