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arXiv · 1312.6309

Diophantine equations in the primes

Brian Cook·Ákos Magyar
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Abstract

Let $\mathfrak{p}=(\mathfrak{p}_1,...,\mathfrak{p}_r)$ be a system of $r$ polynomials with integer coefficients of degree $d$ in $n$ variables $\mathbf{x}=(x_1,...,x_n)$. For a given $r$-tuple of integers, say $\mathbf{s}$, a general local to global type statement is shown via classical Hardy-Littlewood type methods which provides sufficient conditions for the solubility of $\mathfrak{p}(\mathbf{x})=\mathbf{s}$ under the condition that each of the $x_i$'s is prime.

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Brian Cook, Ákos Magyar. 2013-12-21. Diophantine equations in the primes. https://doi.org/10.1007/s00222-014-0508-1

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