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

Giacomo Cherubini ^[1] ; Morten S. Risager ^[1]
1. [1] University of Copenhagen
  
  University of Copenhagen
  
  Dinamarca
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 34, Nº 2, 2018, págs. 655-685
Idioma: inglés
DOI: 10.4171/RMI/1000
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Resumen
- 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.