Irreducible values of polynomials

Lior Bary-Soroker*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)854-874
Number of pages21
JournalAdvances in Mathematics
Volume229
Issue number2
DOIs
StatePublished - 30 Jan 2012
Externally publishedYes

Funding

FundersFunder number
Seventh Framework Programme226135
European Research Council

    Keywords

    • Bateman-Horn conjecture
    • Hilbert's irreducibility theorem
    • Irreducible polynomials
    • Pseudo algebraically closed fields
    • Schinzel's Hypothesis H

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