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On an asymmetric divisor problem with congruence conditions

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Abstract

For fixed positive integersa≠b, natural numbersl 1≤k 1,l 2≤k 2 andn, denote withd a,b (l 1,k 1;l 2,k 2;n) the number of all (υ,ω)∈N2 withν aωb =n,ν≡l 1(modk 1),ω≡l 2(modk 2). In the present paper we establish asymptotic formulas for the Dirichlet summatory function ofd a,b (l 1,k 1;l 2,k 2;n) with both upper and lower estimates of the error term, all of them uniform in the moduli.

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Authors and Affiliations

  1. Sektion Mathematik der Friedrich-Schiller-Universität, DDR-6900, Jena

    Hartmut Menzer

  2. Institut für Mathematik, Universität für Bodenkultur, A-1180, Wien, Austria

    Werner Georg Nowak

Authors
  1. Hartmut Menzer
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  2. Werner Georg Nowak
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Menzer, H., Nowak, W.G. On an asymmetric divisor problem with congruence conditions. Manuscripta Math 64, 107–119 (1989). https://doi.org/10.1007/BF01182087

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