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On the error term for the counting functions of finite Abelian groups

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Abstract

Leta(n) denote the number of non-isomorphic Abelian groups withn elements, and Δ(x) (resp. Δ x ) appropriate error terms in the asymptotic formulas for the counting function\(\sum\nolimits_{n \leqslant x} {a(n)} (resp. \sum\nolimits_{m n \leqslant x} {a(m)} a(n))\). Sharp bounds for

$$\int\limits_1^X {\Delta (x) dx} , \int\limits_1^X {\Delta _{ 1} (x) dx} ,\int\limits_1^X {\Delta _1^2 (x) dx} $$

are given by using results on power moments of the Riemann zeta-function.

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Authors and Affiliations

  1. Katedra matematike RGF-a, Universiteta u Beogradu, Djušina 7, 11000, Beograd, Jugoslavija

    Aleksandar Ivić

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  1. Aleksandar Ivić
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Research financed by the Math. Institute of Belgrade and Rep. Zajed. Serbia

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Ivić, A. On the error term for the counting functions of finite Abelian groups. Monatshefte für Mathematik 114, 115–124 (1992). https://doi.org/10.1007/BF01535578

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  • DOI: https://doi.org/10.1007/BF01535578

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