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<p>This paper extends the Cohen-Ramanujan sum originally defined by Cohen to arbitrary residually finite Dedekind domains. We derive further properties that can be viewed as generalizations of those provided by Zheng [16] and Zheng-Chen-Hong [27]. In particular, we illustrate that the set of the Cohen-Ramanujan sums can be used as a basis for Fourier expansions just as the classical Ramanujan sums can.</p>

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A generalized Ramanujan sum over a residually finite Dedekind domain

  • 期刊论文

  • 发表日期：

    2025年3月18日

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  • T. Qi

摘要

This paper extends the Cohen-Ramanujan sum originally defined by Cohen to arbitrary residually finite Dedekind domains. We derive further properties that can be viewed as generalizations of those provided by Zheng [16] and Zheng-Chen-Hong [27]. In particular, we illustrate that the set of the Cohen-Ramanujan sums can be used as a basis for Fourier expansions just as the classical Ramanujan sums can.