On a two-variable zeta function for number fields
نویسندگان
چکیده
منابع مشابه
On a Two-Variable Zeta Function for Number Fields
This paper studies a two-variable zeta function ZK(w, s) attached to an algebraic number field K, introduced by van der Geer and Schoof [11], which is based on an analogue of the RiemannRoch theorem for number fields using Arakelov divisors. When w = 1 this function becomes the completed Dedekind zeta function ζ̂K(s) of the field K. The function is an meromorphic function of two complex variable...
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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 analogo...
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Abstract. Let K be a global function field with finite constant field Fq of order q. In this paper we develop the analytic theory of a multiple zeta function Zd(K; s1, . . . , sd) in d independent complex variables defined over K. This is the function field analog of the Euler-Zagier multiple zeta function ζd(s1, . . . , sd) of depth d ([Z1]). Our main result is that Zd(K; s1, . . . , sd) has a...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 2003
ISSN: 0373-0956
DOI: 10.5802/aif.1939