On the variance of sums of divisor functions in short intervals
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- by Stephen Lester PDF
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Abstract:
Given a positive integer $n$ the $k$-fold divisor function $d_k(n)$ equals the number of ordered $k$-tuples of positive integers whose product equals $n$. In this article we study the variance of sums of $d_k(n)$ in short intervals and establish asymptotic formulas for the variance of sums of $d_k(n)$ in short intervals of certain lengths for $k=3$ and for $k \ge 4$ under the assumption of the Lindelöf hypothesis.References
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Additional Information
- Stephen Lester
- Affiliation: School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
- Address at time of publication: Department of Mathematics, KTH Royal Institute of Technology, SE-100 44, Stockholm, Sweden
- Email: sjlester@kth.se
- Received by editor(s): February 4, 2015
- Published electronically: August 17, 2016
- Additional Notes: The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement n$^{\text {o}}$ 320755.
- Communicated by: Alexander Iosevich
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 5015-5027
- MSC (2010): Primary 11N37, 11M06
- DOI: https://doi.org/10.1090/proc/12914
- MathSciNet review: 3556248