The hyperbolic circle problem over Heegner points

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.