ar X iv : 0 90 3 . 52 40 v 1 [ m at h . N T ] 3 0 M ar 2 00 9 TRANSCENDENCE OF GENERATING FUNCTIONS WHOSE COEFFICIENTS ARE MULTIPLICATIVE
نویسندگان
چکیده
Let K be a field of characteristic 0, f : N → K be a multiplicative function, and F (z) = P n≥1 f (n)z n ∈ K[[z]] be algebraic over K(z). Then either there is a natural number k and a periodic multiplicative function χ(n) such that f (n) = n k χ(n) for all n, or f (n) is eventually zero. In particular , the generating function of a multiplicative function f : N → K is either transcendental or rational.
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