On the Bateman-Horm Conjecture about Polynomial Rings

Lior Bary-Soroker; Moshe Jarden

On the Bateman-Horm Conjecture about Polynomial Rings

Number Theory 2012-03-06 v1

Authors: Lior Bary-Soroker , Moshe Jarden

Abstract

Given a power $q$ of a prime number $p$ and "nice" polynomials $f_1,...,f_r\in\bbF_q[T,X]$ with $r=1$ if $p=2$ , we establish an asymptotic formula for the number of pairs $(a_1,a_2)\in\bbF_q^2$ such that $f_1(T,a_1T+a_2),...,f_r(T,a_1T+a_2)$ are irreducible in $\bbF_q[T]$ . In particular that number tends to infinity with $q$ .

Keywords

finite fields polynomials over finite fields prime number theory

Cite

@article{arxiv.1203.0726,
  title  = {On the Bateman-Horm Conjecture about Polynomial Rings},
  author = {Lior Bary-Soroker and Moshe Jarden},
  journal= {arXiv preprint arXiv:1203.0726},
  year   = {2012}
}

Comments

To be published in Muenster Journal of Mathematics

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