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On higher-power moments of the error term for the divisor problem with congruence conditions

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Abstract

For a positive integer n, the divisor function with congruence conditions d(n; l 1, M 1, l 2, M 2) denotes the number of factorizations n = n 1 n 2, where each of the factors \({n_i\in\mathbb{N}}\) belongs to a prescribed congruence class l i modulo M i   (i = 1, 2). In this paper we study the higher power moments of the error term in the asymptotic formula of \({\sum\nolimits_{n\leq M_1M_2x}d(n;l_1,M_1,l_2,M_2)}\) .

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Authors and Affiliations

  1. Department of Mathematics, Shandong University, Jinan, 250100, Shandong, People’s Republic of China

    Kui Liu

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  1. Kui Liu
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Correspondence to Kui Liu.

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Communicated by J. Schoißengeier.

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Liu, K. On higher-power moments of the error term for the divisor problem with congruence conditions. Monatsh Math 163, 175–195 (2011). https://doi.org/10.1007/s00605-010-0221-0

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  • DOI: https://doi.org/10.1007/s00605-010-0221-0

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