On the variance of the error term in the hyperbolic circle problem
Giacomo CherubiniUniversity of Copenhagen, Denmark
Morten S. RisagerUniversity of Copenhagen, Denmark
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. 655–685DOI 10.4171/RMI/1000