Diophantine equations in the primes

2013/12/21 by Brian Cook, Ákos Magyar · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Combinatorics #Degree (music) #Diophantine equation #Discrete mathematics #Integer (computer science) #Mathematical Dynamics and Fractals #Mathematics #Prime (order theory) #Prime number #Type (biology) #math.NT

paper · pdf · doi:10.1007/s00222-014-0508-1

arxiv created 2013/12/21 · openalex publication_date 2014/04/22 · arxiv updated 2015/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Let \mathfrakp=(\mathfrakp₁,...,\mathfrakp_r) be a system of r polynomials with integer coefficients of degree d in n variables x=(x₁,...,x_n). For a given r-tuple of integers, say s, a general local to global type statement is shown via classical Hardy-Littlewood type methods which provides sufficient conditions for the solubility of \mathfrakp(x)=s under the condition that each of the x_i's is prime.

Citations

• Bounded gaps between primes
• Algebraic Geometry

Cited by

• Finite Saturation for Unirational Varieties
• Rational lines on cubic hypersurfaces