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<p>In this paper, we further investigate Dirichlet characters and additive characters in the field of residually finite Dedekind domains. We present a novel variant of Tóth’s identity, specifically, a Menon-type identity for arithmetic functions involving both Dirichlet characters and additive characters in residually finite Dedekind domains. It can be viewed as an extension of Chen and Zheng’s identity (2022). As an application, we provide a version of the Menon-type identity in the ring of integers of a number field.</p>

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A generalization of a Menon-type identity by Tóth in residually finite Dedekind domains

  • 期刊论文

  • 发表日期：

    2025年4月8日

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  • Tianfang Qi,
  • Man Chen

摘要

In this paper, we further investigate Dirichlet characters and additive characters in the field of residually finite Dedekind domains. We present a novel variant of Tóth’s identity, specifically, a Menon-type identity for arithmetic functions involving both Dirichlet characters and additive characters in residually finite Dedekind domains. It can be viewed as an extension of Chen and Zheng’s identity (2022). As an application, we provide a version of the Menon-type identity in the ring of integers of a number field.