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On the variance of sums of divisor functions in short intervals
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). Tel Aviv University, Israel.
2016 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 144, no 12, 5015-5027 p.Article in journal (Refereed) Published
Abstract [en]

Given a positive integer n the k-fold divisor function dk(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 >= 4 under the assumption of the Lindelof hypothesis.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2016. Vol. 144, no 12, 5015-5027 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-196590DOI: 10.1090/proc/12914ISI: 000386136300001Scopus ID: 2-s2.0-84992393713OAI: oai:DiVA.org:kth-196590DiVA: diva2:1047638
Funder
EU, FP7, Seventh Framework Programme, 320755
Note

QC 20161118

Available from: 2016-11-18 Created: 2016-11-17 Last updated: 2016-11-18Bibliographically approved

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