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We introduce a Dedekind-like zeta function for the algebra of bicomplex numbers. By using the idempotent representations for such numbers, we identify this function with the one associated to a product of copies of the field of Gaussian rationals. This approach is substantially different from the one due to Rochon.

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A Zeta Function for the Bicomplex Algebra

  • 会议论文

  • 发表日期：

    2025年

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  • Ahmed Sebbar,
  • Daniele C. Struppa,
  • Adrian Vajiac,
  • Mihaela Vajiac

摘要

We introduce a Dedekind-like zeta function for the algebra of bicomplex numbers. By using the idempotent representations for such numbers, we identify this function with the one associated to a product of copies of the field of Gaussian rationals. This approach is substantially different from the one due to Rochon.