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December 2004 A Bicomplex Riemann Zeta Function
Dominic ROCHON
Tokyo J. Math. 27(2): 357-369 (December 2004). DOI: 10.3836/tjm/1244208394


In this work we use a commutative generalization of complex numbers, called bicomplex numbers, to introduce a holomorphic Riemann zeta function of two complex variables satisfying the complexified Cauchy-Riemann equations. Furthermore, we establish a bicomplex Riemann hypothesis equivalent to the complex Riemann hypothesis of one variable and we obtain a bicomplex Euler Product.


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Dominic ROCHON. "A Bicomplex Riemann Zeta Function." Tokyo J. Math. 27 (2) 357 - 369, December 2004.


Published: December 2004
First available in Project Euclid: 5 June 2009

zbMATH: 1075.30025
MathSciNet: MR2107508
Digital Object Identifier: 10.3836/tjm/1244208394

Primary: 30G35‎
Secondary: 32A30

Rights: Copyright © 2004 Publication Committee for the Tokyo Journal of Mathematics

Vol.27 • No. 2 • December 2004
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