Numbers Related to Bernoulli-Goss Numbers

Mohamed Ould Douh Benough^1,

¹Département de Mathématique-Informatique, Université des Sciences, de Technologie et de Médecine, Nouakchott, Mauritanie

Cite this paper:
Mohamed Ould Douh Benough. Numbers Related to Bernoulli-Goss Numbers. Turkish Journal of Analysis and Number Theory. 2014; 2(1):13-18. doi: 10.12691/tjant-2-1-4

Abstract

In this paper, we generalize a Goss result appeared in ([5], page 325, line 19, for i=1 ), and give a characterization of some numbers of Bernoulli-Goss [5] by introducing the special numbers M(d).

Keywords:
Bernoulli-Goss Carlitz Module congruence irreducible polynomials.

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References:

[1]	G. Anderson. Log-Algebraicity of Twisted A-Harmonic Series and Special Values of L-series in Characteristic p, J.Number Theory 60(1996), 165-209.
[2]	B. Anglès and L. Taelman. On a Problem à la Kummer-Vandiver for function fields, to appear in J.Number Theory (2012).
[3]	L. Carlitz. An analogue of the Bernoulli polynomials .Duke Math. J.,8:405-412, 1941.
[4]	Ernst-Ulrich Gekeler. On power sums of polynomials over finite fields, J.Number Theory 30(1988), 11-26.
[5]	D. Goss. Basic Structures of Function Field Arithmetic , Ergebnisse der Mathematik und ihrer Grenzgebiete, vol.35, Springer,Berlin, 1996.
[6]	Ireland K, Rosen M I. A classical introduction to modern number theory. New York: Springer, 1982.
[7]	M. Mignotte. Algébre Concrete, Cours et exercices.
[8]	M. Rosen. Number theory in function fields}. Springer-Verlag, New York, 2002.
[9]	J. T. Sheats. On the Riemann hypothesis for the Goss Zeta function for q[T], J Number Theory 71(1); (1998), 121-157.
[10]	D. Thakur. Zeta measure associated to, q[T] J.Number Theory 35(1990), 1-17.
[11]	Mohamed Ould Douh Benough. Corps de Fonctions Cyclotomiques, Thèse Doctorat de l'Université de Caen, France (2012).