Asymptotic formula for the convolution of a generalized divisor function |
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| Authors: | V A Bykovskii D A Frolenkov |
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| Institution: | 1. Institute of Applied Mathematics (Khabarovsk Branch), Far Eastern Branch, Russian Academy of Sciences, ul. Dzerzhinskogo 54, Khabarovsk, 680000, Russia
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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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