Abstract Let S , H X be groups. For two given biadditive functions A : 2 → B and for unknown mappings T g we will study the functional equation ( x ), y )) = x, )), ∈ S, which is a generalization of orthogonality in Hilbert spaces.

Abstract Let X , Y be linear spaces over a field $${\mathbb {K}}$$ K . Assume that $$f :X^2\rightarrow Y$$ f : X 2 → Y satisfies the general equation with respect...

1. L(s, χ) for even Dirichlet characters 2. L(s, χ) for odd Dirichlet characters 3. Dedekind zeta function ζ o (s) for Gaussian integers o 4. Grossencharacter L-functions L-functions for Gaussian integers We try to imitate the argument used by Riemann for proving the analytic continuation of ζ(s) and its functional equation π −s/2 Γ(s 2) ζ(s) = π −(1−s)/2 Γ(1−s 2) ζ(1 − s) from the integral rep...

Let [a, b] be any bounded closed real interval. The class of all continuous, nondecreasing, associative functions M : [a, b] → [a, b] fulfilling the boundary conditions M(a, a) = a and M(b, b) = b is described.