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CM-points and lattice counting on arithmetic compact Riemann surfaces
dc.contributor.author | Alsina Aubach, Montserrat |
dc.contributor.author | Chatzakos, Dimitrios |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2020-03-04T14:51:02Z |
dc.date.available | 2020-03-04T14:51:02Z |
dc.date.issued | 2020-07 |
dc.identifier.citation | Alsina, M.; Chatzakos, D. CM-points and lattice counting on arithmetic compact Riemann surfaces. "Journal of number theory", July 2020, vol. 212, p. 339-353. |
dc.identifier.issn | 0022-314X |
dc.identifier.other | https://arxiv.org/pdf/1808.01318.pdf |
dc.identifier.uri | http://hdl.handle.net/2117/179201 |
dc.description.abstract | Let $X(D,1) =\Gamma(D,1) \backslash \mathbb{H}$ denote the Shimura curve of level $N=1$ arising from an indefinite quaternion algebra of fixed discriminant $D$. We study the discrete average of the error term in the hyperbolic circle problem over Heegner points of discriminant $d <0$ on $X(D,1)$ as $d \to -\infty$. We prove that if $|d|$ is sufficiently large compared to the radius $r \approx \log X$ of the circle, we can improve on the classical $O(X^{2/3})$-bound of Selberg. Our result extends the result of Petridis and Risager for the modular surface to arithmetic compact Riemann surfaces. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 4.0 International |
dc.rights | ©2020. Elsevier |
dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística |
dc.subject.lcsh | Spectral theory (Mathematics) |
dc.subject.lcsh | Riemann surfaces |
dc.subject.lcsh | Arithmetic groups |
dc.subject.lcsh | Automorphisms |
dc.subject.other | Discontinuous groups and automorphic forms |
dc.subject.other | Arithmetic groups |
dc.subject.other | Spectral theory |
dc.title | CM-points and lattice counting on arithmetic compact Riemann surfaces |
dc.type | Article |
dc.subject.lemac | Teoria espectral (Matemàtica) |
dc.subject.lemac | Riemann, Superfícies de |
dc.subject.lemac | Automorfismes |
dc.contributor.group | Universitat Politècnica de Catalunya. TN - Grup de Recerca en Teoria de Nombres |
dc.identifier.doi | 10.1016/j.jnt.2019.11.009 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::37 Dynamical systems and ergodic theory::37D Dynamical systems with hyperbolic behavior |
dc.subject.ams | Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory |
dc.relation.publisherversion | https://www.sciencedirect.com/science/article/pii/S0022314X19304093 |
dc.rights.access | Open Access |
local.identifier.drac | 27020161 |
dc.description.version | Postprint (author's final draft) |
dc.relation.projectid | info:eu-repo/grantAgreement/MINECO//MTM2015-63829-P/ES/LA CONJETURA DE BIRCH Y SWINNERTON-DYER/ |
local.citation.author | Alsina, M.; Chatzakos, D. |
local.citation.publicationName | Journal of number theory |
local.citation.volume | 212 |
local.citation.startingPage | 339 |
local.citation.endingPage | 353 |
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