On the restricted divisor function in arithmetic progressions

Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We obtain several asymptotic estimates for the sums of the restricted divisor function τM,N(k) =#{1≤m≤M, 1 ≤n≤N: mn = k} over short arithmetic progressions, which improve some results of J. Truelsen. Such estimates are motivated by the links with the pair correlation problem for fractional parts of the quadratic function αk2, k = 1, 2, . . . with a real α.

Original languageEnglish
Pages (from-to)231-238
Number of pages8
JournalRevista Matematica Iberoamericana
Volume28
Issue number1
DOIs
Publication statusPublished - 2012

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