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An analogue of Ramanujan’s sum with respect to regular integers (modr)

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Abstract

An integer a is said to be regular (modr) if there exists an integer x such that a 2 x≡a (mod r). In this paper we introduce an analogue of Ramanujan’s sum with respect to regular integers (modr) and show that this analogue possesses properties similar to those of the usual Ramanujan’s sum.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Tampere, Kalevantie 4, 33014, Tampere, Finland

    Pentti Haukkanen

  2. Institute of Mathematics and Informatics, University of Pécs, Ifjúság u. 6, 7624, Pécs, Hungary

    László Tóth

Authors
  1. Pentti Haukkanen
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  2. László Tóth
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Correspondence to Pentti Haukkanen.

Additional information

Financial support from the Magnus Ehrnrooth Foundation is gratefully acknowledged.

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Haukkanen, P., Tóth, L. An analogue of Ramanujan’s sum with respect to regular integers (modr). Ramanujan J 27, 71–88 (2012). https://doi.org/10.1007/s11139-011-9327-9

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  • DOI: https://doi.org/10.1007/s11139-011-9327-9

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