Multiple arithmetic functions in function fields.

Let F be a field of characteristic p ≥ 0 , and let K [ T ] + be the set of monic polynomials in the polynomial ring K[T]. We define the Dirichlet product of F-valued arithmetic functions on K [ T ] + and consider the ring of F-valued arithmetic functions. The purpose of this paper is to prove an analogue of the ABC conjecture in this ring. [ABSTRACT FROM AUTHOR]