Under GRH and analytic continuation hypotheses, the paper completes a decorrelation conjecture for products of Hecke eigenforms and proves new ℓ^p-norm bounds for quadratic forms in the Hecke basis.
The hyperbolic circle problem over Heegner points
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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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Quadratic forms of modular forms
Under GRH and analytic continuation hypotheses, the paper completes a decorrelation conjecture for products of Hecke eigenforms and proves new ℓ^p-norm bounds for quadratic forms in the Hecke basis.