Resumen de 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 eα(s) the fractional integral to order α of e(s). We prove that for any small α>0 the asymptotic variance of eα(s) is finite, and given by an explicit expression. Moreover, we prove that eα(s) has a limiting distribution.