Skopje, Makedonija ABOUT CHARACTERS ON VILENKIN ...

ABOUT CHARACTERS ON VILENKIN GROUPS 39
of the corresponding coefficients. Addition of elements x =(x j ) j∈N0 and y =
(y j ) j∈N0 in G we denote by + and define it by component addition. Component
addition for arbitrary coordinate j ∈ N 0 is addition mod p j+1 .
For arbitrary n ∈ N given by (5) and arbitrary x ∈ g given by (3) we have
χ n (x) =
∞∏
j=0
χ n j
m j
(x), 0 ≤ n j