Comptes Rendus
no. 17-18
Number Theory
Decompositions into sums of two irreducibles in Fq[t]
[Décompositions en sommes de deux polynômes irréductibles dans Fq[t]]

Présenté par : Jean-Pierre Serre

Andreas O. Bender1
1 Korea Institute for Advanced Study, Seoul 130-722, South Korea
Comptes Rendus. Mathématique, Volume 346 (2008) no. 17-18, pp. 931-934.

A monic polynomial in Fq[t] of degree n over a finite field Fq of odd characteristic is the sum of two monic irreducibles in Fq[t] of degrees n and n−1, provided q is larger than an explicitly given bound in terms of n.

Un polynôme unitaire f∈Fq[t] de degré n à coefficients dans un corps fini Fq de caractéristique différente de 2 s'écrit comme une somme f=g+h, où g,h∈Fq[t] sont des polynômes unitaires irréductibles de degrés n et n−1, dès que q est plus grand qu'une borne explicite dépendant uniquement de n.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.07.025

Andreas O. Bender 1

1 Korea Institute for Advanced Study, Seoul 130-722, South Korea 
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Andreas O. Bender. Decompositions into sums of two irreducibles in $ {\mathbf{F}}_{q}[t]$. Comptes Rendus. Mathématique, Volume 346 (2008) no. 17-18, pp. 931-934. doi : 10.1016/j.crma.2008.07.025. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.07.025/

[1] A.O. Bender, Representing an element in Fq[t] as the sum of two irreducibles in Fqs[t], submitted for publication

[2] A.O. Bender; O. Wittenberg A potential analogue of Schinzel's hypothesis for polynomials with coefficients in Fq[t], Int. Math. Res. Not., Volume 36 (2005), pp. 2237-2248 (also available from) | arXiv

[3] G.W. Effinger; D.R. Hayes Additive Number Theory of Polynomials Over a Finite Field, Oxford University Press, New York, NY, 1991

[4] D. Eisenbud Commutative Algebra With a View Toward Algebraic Geometry, Graduate Texts in Mathematics, vol. 150, Springer-Verlag, New York, NY, 1995

[5] A. Hurwitz Über Riemann'sche Flächen mit gegebenen Verzweigungspunkten, Math. Ann., Volume 39 (1891), pp. 1-61 (and Math. Werke, Band 1/XXI, Birkhäuser, Basel, 1932)

Cité par 4 documents. Sources : zbMATH

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