Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6426004 | Advances in Mathematics | 2012 | 21 Pages |
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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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Lior Bary-Soroker,