The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Revista Matemática Iberoamericana


Full-Text PDF (389 KB) | Metadata | Table of Contents | RMI summary
Online access to the full text of Revista Matemática Iberoamericana is restricted to the subscribers of the journal, who are encouraged to communicate their IP-address(es) to their agent or directly to the publisher at
subscriptions@ems-ph.org
Volume 34, Issue 2, 2018, pp. 655–685
DOI: 10.4171/RMI/1000

Published online: 2018-05-28

On the variance of the error term in the hyperbolic circle problem

Giacomo Cherubini[1] and Morten S. Risager[2]

(1) University of Copenhagen, Denmark
(2) University of Copenhagen, Denmark

Let $e(s)$ be the error term of the hyperbolic circle problem, and denote by $e_\alpha(s)$ the fractional integral to order $\alpha$ of $e(s)$. We prove that for any small $\alpha>0$ the asymptotic variance of $e_\alpha(s)$ is finite, and given by an explicit expression. Moreover, we prove that $e_\alpha(s)$ has a limiting distribution.

Keywords: Hyperbolic lattice points, Selberg’s pre-trace formula, fractional integration

Cherubini Giacomo, Risager Morten: On the variance of the error term in the hyperbolic circle problem. Rev. Mat. Iberoam. 34 (2018), 655-685. doi: 10.4171/RMI/1000