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Advances in Applied Clifford Algebras

, Volume 23, Issue 1, pp 237–251 | Cite as

A Multicomplex Riemann Zeta Function

  • Frederick Lyall Reid
  • Robert A. Van Gorder
Article

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.

Keywords

Multicomplex number system Multicomplex analysis Riemann zeta function 

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Copyright information

© Springer Basel 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Central FloridaOrlandoUSA

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