Revista Integración, temas de matemáticas.
Vol. 35 No. 2 (2017): Revista Integración, temas de matemáticas
Research and Innovation Articles

Theorem of Dirichlet on Fq [t]

Harold Gamero
Universidad del Atlántico
Bio
Jaider Blanco
Universidad del Norte
Bio
Gabriel Vergara
Universidad del Atlántico
Bio

Published 2018-03-06

Keywords

  • Characters,
  • Series-L,
  • M¨obius inversion formula

How to Cite

Gamero, H., Blanco, J., & Vergara, G. (2018). Theorem of Dirichlet on Fq [t]. Revista Integración, Temas De matemáticas, 35(2), 163–188. https://doi.org/10.18273/revint.v35n2-2017003

Abstract

In this paper we prove the existence of infinite unit irreducible prime polynomials on the finite field Fq by Pollack through of characters and L-series.

Downloads

Download data is not yet available.

References

[1] Albis V.S., Lecciones sobre la Aritmética de Polinomios, Policopiado, Universidad Nacional de Colombia, 2002.

[2] Apostol T.M., Introduction to Analytic Number Theory, Springer-Verlag, New York, 1998.

[3] Dirichlet P.G.L., "Beweis des Satzes dass jede unbegrenzte arithmetische Progression, deren erstes Glied und Differenz ganze Zahlen ohne gemeinschlaftichen Factor sind unendliche viele Primzahlen enthglt", Abhand. Ak. Wiss. Berlin, 1 (1837), 45-81, [Werke, 1: 315-342].

[4] Ireland K. and Rosen M., A Classical Introduction to Modern Number Theory, Springer-Verlag, New York, 1990.

[5] Pollack P., An Elementary Proof of Dirichlet's Theorem in the Polynomial Setting, Preimpreso.

[6] Rosen M., Number Theory in Function Fields, Springer-Verlag, New York, 2002.

[7] Shapiro H.N.,"On primes in Arithmetic progression II", Ann. of Math. (2) 52 (1950), No. 1, 231-243.