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On sums of generalized Ramanujan sums

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  • Yusuke Fujisawa

    (Nagoya University)

Abstract

Ramanujan sums have been studied and generalized by several authors. For example, Nowak [8] studied these sums over quadratic number fields, and Grytczuk [4] defined that on semigroups. In this note, we deduce some properties on sums of generalized Ramanujan sums and give examples on number fields. In particular, we have a relational expression between Ramanujan sums and residues of Dedekind zeta functions.

Suggested Citation

  • Yusuke Fujisawa, 2015. "On sums of generalized Ramanujan sums," Indian Journal of Pure and Applied Mathematics, Springer, vol. 46(1), pages 1-10, February.
    • Handle: RePEc:spr:indpam:v:46:y:2015:i:1:d:10.1007_s13226-015-0103-1
    DOI: 10.1007/s13226-015-0103-1
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    Keywords

    Ramanujan sums; arithmetical functions;

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