TY - JOUR

T1 - Irreducible values of polynomials

AU - Bary-Soroker, Lior

N1 - Funding Information:
Part of this work was done while the author was a Lady Davis postdoc fellow in the Hebrew University of Jerusalem. While writing this work the author was an Alexander von Humboldt postdoc fellow in the Institut für Experimentelle Mathematik in Duisburg-Essen University. This research is partially supported by a grant from the ERC.

PY - 2012/1/30

Y1 - 2012/1/30

N2 - Schinzel's Hypothesis H is a general conjecture in number theory on prime values of polynomials that generalizes, e.g., the twin prime conjecture and Dirichlet's theorem on primes in arithmetic progression. We prove a quantitative arithmetic analog of this conjecture for polynomial rings over pseudo algebraically closed fields. This implies results over large finite fields via model theory. A main tool in the proof is an irreducibility theorem à la Hilbert.

AB - Schinzel's Hypothesis H is a general conjecture in number theory on prime values of polynomials that generalizes, e.g., the twin prime conjecture and Dirichlet's theorem on primes in arithmetic progression. We prove a quantitative arithmetic analog of this conjecture for polynomial rings over pseudo algebraically closed fields. This implies results over large finite fields via model theory. A main tool in the proof is an irreducibility theorem à la Hilbert.

KW - Bateman-Horn conjecture

KW - Hilbert's irreducibility theorem

KW - Irreducible polynomials

KW - Pseudo algebraically closed fields

KW - Schinzel's Hypothesis H

UR - http://www.scopus.com/inward/record.url?scp=82355175213&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2011.10.006

DO - 10.1016/j.aim.2011.10.006

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AN - SCOPUS:82355175213

SN - 0001-8708

VL - 229

SP - 854

EP - 874

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 2

ER -