Averaging over Heegner Points in the Hyperbolic Circle Problem
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For Gamma = PSL2(Z) the hyperbolic circle problem aims to estimate the number of elements of the orbit Gamma z inside the hyperbolic disc centred at z with radius cosh(-1) (X/2). We show that, by averaging over Heegner points z of discriminant D, Selberg's error term estimate can be improved, if D is large enough. The proof uses bounds on spectral exponential sums, and results towards the sup-norm conjecture of eigenfunctions, and the Lindelof conjecture for twists of the L-functions attached to Maass cusp forms.
Originalsprog | Engelsk |
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Tidsskrift | International Mathematics Research Notices |
Vol/bind | 2018 |
Udgave nummer | 16 |
Sider (fra-til) | 4942-4968 |
ISSN | 1073-7928 |
DOI | |
Status | Udgivet - 2018 |
Links
- https://arxiv.org/pdf/1610.09393.pdf
Accepteret manuskript
ID: 209574604