Diophantine equations in the primes

• 成果类型: Article
• 署名作者: Cook, Brian; Magyar, Akos
• 署名单位: University of Wisconsin System; University of Wisconsin Madison; University of British Columbia
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0508-1
• 发表日期: 2014
• 页码: 701-737
• 关键词: linear-equations; integer points; density

摘要

Let p = (p(1), ... , p(r)) be a system of r polynomials with integer coefficients of degree d in n variables x = (x(1), ... , 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 p(x) = s under the condition that each of the x(i)'s is prime.