On the variance of the error term in the hyperbolic circle problem
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 December 2015
 arXiv:
 arXiv:1512.04779
 Bibcode:
 2015arXiv151204779C
 Keywords:

 Mathematics  Number Theory;
 11P21;
 11F72
 EPrint:
 26 pages