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Asymptotic formula for the convolution of a generalized divisor function

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Abstract

An asymptotic formula is obtained for the sum of terms σ it (n)σ-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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Authors and Affiliations

  1. Institute of Applied Mathematics (Khabarovsk Branch), Far Eastern Branch, Russian Academy of Sciences, ul. Dzerzhinskogo 54, Khabarovsk, 680000, Russia

    V. A. Bykovskii & D. A. Frolenkov

Authors
  1. V. A. Bykovskii
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  2. D. A. Frolenkov
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Correspondence to V. A. Bykovskii.

Additional information

Original Russian Text © V.A. Bykovskii, D.A. Frolenkov, 2015, published in Doklady Akademii Nauk, 2015, Vol. 465, No. 2, pp. 137–140.

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Bykovskii, V.A., Frolenkov, D.A. Asymptotic formula for the convolution of a generalized divisor function. Dokl. Math. 92, 670–673 (2015). https://doi.org/10.1134/S1064562415060071

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  • DOI: https://doi.org/10.1134/S1064562415060071

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