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arXiv · 1310.5275

Polynomials and Primes in Generalized Arithmetic Progressions (Revised Version)

Ernie Croot·Neil Lyall·Alex Rice
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Abstract

We provide upper bounds on the density of a symmetric generalized arithmetic progression lacking nonzero elements of the form h(n) for natural numbers n, or h(p) with p prime, for appropriate polynomials h with integer coefficients. The prime variant can be interpreted as a multi-dimensional, polynomial extension of Linnik's Theorem. This version is a revision of the published version. Most notably, the properness hypotheses have been removed from Theorems 2 and 3, and the numerology in Theorem 2 has been improved.

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Ernie Croot, Neil Lyall, Alex Rice. 2013-10-19. Polynomials and Primes in Generalized Arithmetic Progressions (Revised Version). https://arxiv.org/abs/1310.5275

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