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

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 نشر من قبل Morten S. Risager
 تاريخ النشر 2015
  مجال البحث
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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 asymptotic variance of $e_alpha(s)$ is finite, and given by an explicit expression. Moreover, we prove that $e_alpha(s)$ has a limiting distribution.



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