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.
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