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A Multicomplex Riemann Zeta Function

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Abstract

After reviewing properties of analytic functions on the multicomplex number space \({\mathbb{C}_{k}}\) (a commutative generalization of the bicomplex numbers \({\mathbb{C}_{2}}\) ), a multicomplex Riemann zeta function is defined through analytic continuation. Properties of this function are explored, and we are able to state a multicomplex equivalence to the Riemann hypothesis.

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Authors and Affiliations

  1. Department of Mathematics, University of Central Florida, Orlando, FL, 32816, USA

    Frederick Lyall Reid & Robert A. Van Gorder

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  1. Frederick Lyall Reid
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  2. Robert A. Van Gorder
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Correspondence to Robert A. Van Gorder.

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Reid, F.L., Van Gorder, R.A. A Multicomplex Riemann Zeta Function. Adv. Appl. Clifford Algebras 23, 237–251 (2013). https://doi.org/10.1007/s00006-012-0369-x

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  • DOI: https://doi.org/10.1007/s00006-012-0369-x

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