Irreducible values of polynomials |
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Authors: | Lior Bary-Soroker |
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Institution: | Institut für Experimentelle Mathematik, Universität Duisburg-Essen, Ellernstrasse 29, D-45326 Essen, Germany |
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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. |
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Keywords: | Irreducible polynomials Pseudo algebraically closed fields Schinzel's Hypothesis H Hilbert's irreducibility theorem Bateman–Horn conjecture |
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