  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.
