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The aim of this paper is to point out a number-theoretical property of a certain product of values taken by an abelian function at points of finite order of the abelian variety on which the abelian function is considered We use the theory of power residues and the theory of complex multiplication, and the result is somewhat similar to the so-called Stickelberger's relation in the theory of Gauss sums. A related investigation was previously made by the author in a special case of elliptic curves .doi:10.1017/s0027763000011843 fatcat:vppfeze6vbeh3cxxva47wtuwh4