Tokyo Journal of Mathematics

A Bicomplex Riemann Zeta Function

Dominic ROCHON

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Abstract

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.

Article information

Source
Tokyo J. of Math. Volume 27, Number 2 (2004), 357-369.

Dates
First available in Project Euclid: 5 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1244208394

Digital Object Identifier
doi:10.3836/tjm/1244208394

Mathematical Reviews number (MathSciNet)
MR2107508

Zentralblatt MATH identifier
1075.30025

Subjects
Primary: 30G35: Functions of hypercomplex variables and generalized variables
Secondary: 32A30: Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30) {For functions of several hypercomplex variables, see 30G35}

Citation

ROCHON, Dominic. A Bicomplex Riemann Zeta Function. Tokyo J. of Math. 27 (2004), no. 2, 357--369. doi:10.3836/tjm/1244208394. https://projecteuclid.org/euclid.tjm/1244208394


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