Doklady Mathematics

, Volume 92, Issue 3, pp 670–673 | Cite as

Asymptotic formula for the convolution of a generalized divisor function

Mathematics

Abstract

An asymptotic formula is obtained for the sum of terms σ it (n-it (N - n) (t is real) over 0 < n < N with a remainder estimated by O ε((1+|t|)1+ε N 3/4+ε) for any ε > 0. As a consequence, Porter’s result on a power scale for the average number of steps in the Euclidean algorithm is improved.

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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Institute of Applied Mathematics (Khabarovsk Branch), Far Eastern BranchRussian Academy of SciencesKhabarovskRussia

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