On the Bateman-Horm Conjecture about Polynomial Rings

Details On the Bateman-Horm Conjecture about Polynomial Rings On the Bateman-Horm Conjecture about Polynomial Rings

2012-03-04

arxiv.org/abs/1203.0726v1

Mathematics

Number Theory

To be published in Muenster Journal of Mathematics

Scientific paper

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 $q$.

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