Hichem Gargoubi ; Sayed Kossentini - Bicomplex numbers as a normal complexified f-algebra

cm:9312 - Communications in Mathematics, May 12, 2022, Volume 30 (2022), Issue 1 - https://doi.org/10.46298/cm.9312
Bicomplex numbers as a normal complexified f-algebra

Authors: Hichem Gargoubi ; Sayed Kossentini

The algebra B of bicomplex numbers is viewed as a complexification of the Archimedean f-algebra of hyperbolic numbers D. This lattice-theoretic approach allows us to establish new properties of the so-called D-norms. In particular, we show that D-norms generate the same topology in B. We develop the D-trigonometric form of a bicomplex number which leads us to a geometric interpretation of the nth roots of a bicomplex number in terms of polyhedral tori. We use the concepts developed, in particular that of Riesz subnorm of a D-norm, to study the uniform convergence of the bicomplex zeta and gamma functions. The main result of this paper is the generalization to the bicomplex case of the Riemann functional equation and Euler's reflection formula.

Volume: Volume 30 (2022), Issue 1
Published on: May 12, 2022
Accepted on: April 6, 2022
Submitted on: June 18, 2020
Keywords: Mathematics - Functional Analysis,Mathematics - Rings and Algebras


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