Short interval asymptotics for a class of arithmetic functions |
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| Authors: | Mübariz Z. Garaev Florian Luca Werner Georg Nowak |
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| Affiliation: | 9201. Instituto de Matemáticas UNAM, Campus Morelia, Ap. Postal 61-3 (Xangari), CP 58089, Morelia, Michoacán, México
9203. Institut für Mathematik, Department für Integrative Biologie, Universit?t für Bodenkultur, Gregor Mendel-Stra?e 33, 1180 Wien, Austria
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| Abstract: | Summary We provide a general asymptotic formula which permits applications to sums like ]]>]]>]]>]]>]]>]]>$]]>]]> sum_{x< nle x+y} big(d(n)big)^2, quad sum_{x< nle x+y} d(n^3),quad sum_{x< nle x+y}big(r(n)big)^2, quad sum_{x< nle x+y}r(n^3), $$ where $d(n)$ and $r(n)$ are the usual arithmetic functions (number of divisors, sums of two squares), and $y$ is small compared to~$x$. |
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| Keywords: | arithmetic functions short intervals |
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