On the irreducibility of the two variable zeta-function for curves over finite fields
نویسنده
چکیده
In [P] R. Pellikaan introduced a two variable zeta-function Z(t, u) for a curve over a finite field Fq which, for u = q, specializes to the usual zeta-function and he proved, among other things, rationality: Z(t, u) = (1 − t)−1(1 − ut)−1P (t, u) with P (t, u) ∈ Z[t, u]. We prove that P (t, u) is absolutely irreducible. This is motivated by a question of J. Lagarias and E. Rains about an analogous two variable zetafunction for number fields. MSC2000: 11G20 (primary), 14G10 (secondary)
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