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

Giacomo Cherubini, Morten S. Risager

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 asymptot…