A Local - Global Theorem on Periodic Maps
نویسندگان
چکیده
Abstract. Let ψ1, . . . , ψk be maps from Z to an additive abelian group with positive periods n1, . . . , nk respectively. We show that the function ψ1 + · · · + ψk is constant if ψ1(x) + · · · + ψk(x) equals a constant for |S| consecutive integers x where S = {r/ns : r = 0, . . . , ns −1; s = 1, . . . , k}. This local-global theorem extends a previous result [Math. Res. Lett. 11(2004), 187–196], and its proof involves linear recurrences and algebraic integers.
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تاریخ انتشار 2004