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

  • Giacomo Cherubini

    University of Copenhagen, Denmark
  • Morten S. Risager

    University of Copenhagen, Denmark

Abstract

Let be the error term of the hyperbolic circle problem, and denote by the fractional integral to order of . We prove that for any small the asymptotic variance of is finite, and given by an explicit expression. Moreover, we prove that has a limiting distribution.

Cite this article

Giacomo Cherubini, Morten S. Risager, On the variance of the error term in the hyperbolic circle problem. Rev. Mat. Iberoam. 34 (2018), no. 2, pp. 655–685

DOI 10.4171/RMI/1000