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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Institution: | 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 <InlineEquation ID=IE"1"><EquationSource Format="TEX"><!CDATA<InlineEquation
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\sum_{x< n\le x+y} \big(d(n)\big)^2, \quad \sum_{x< n\le x+y} d(n^3),\quad \sum_{x< n\le x+y}\big(r(n)\big)^2, \quad \sum_{x<
n\le 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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