Linear Combinations of ζ(s)/Πs Over Fq(x), where 1 ≤ s ≤ q − 2

Carlitz defined both a function ζ and a formal power series Π over Fq, analogous to the Riemann function ζ and to the real number π. Yu used Drinfeld modules to show the fraction ζ(s)/Πs is transcendental over Fq(x), when s is an integer not divisible by q − 1. In this paper we use the automata theo...

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Bibliographic Details
Published in:Journal of number theory 1995-08, Vol.53 (2), p.272-299
Main Author: Berthe, V.
Format: Article
Language:English
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Summary:Carlitz defined both a function ζ and a formal power series Π over Fq, analogous to the Riemann function ζ and to the real number π. Yu used Drinfeld modules to show the fraction ζ(s)/Πs is transcendental over Fq(x), when s is an integer not divisible by q − 1. In this paper we use the automata theory and Christol, Kamae, Mendes France and Rauzy theorem to prove the linear independence over Fq(x) of the fraction ζ(s)/Πs, for all integers s in [1, q − 2].
ISSN:0022-314X
1096-1658
DOI:10.1006/jnth.1995.1091