文献类型：期刊文献

英文题名：SMALL PRIME SOLUTIONS OF A DIOPHANTINE EQUATION WITH ONE PRIME AND FIVE CUBES OF PRIMES

作者：Li, Weiping[1]

第一作者：李伟平

通讯作者：Li, WP[1]

机构：[1]Henan Univ Econ & Law, Dept Math & Informat Sci, Zhengzhou 450046, Peoples R China

第一机构：河南财经政法大学数学与信息科学学院

通讯机构：[1]corresponding author), Henan Univ Econ & Law, Dept Math & Informat Sci, Zhengzhou 450046, Peoples R China.|[1048425]河南财经政法大学数学与信息科学学院;[10484]河南财经政法大学;

年份：2021

卷号：64

期号：1

起止页码：47-69

外文期刊名：FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI

收录：Scopus(收录号：2-s2.0-85109019398);WOS:【ESCI(收录号:WOS:000635157600004)】；

基金：This work was supported by the National Natural Science Foundation of China (Grant No.11371122,11471112), Key Scientific Research Projects Plan of Henan Higher Education Institutions (19A110001), 2016 Young Talents Fund of HUEL. The author is grateful to the referees for helpful comments and suggestions.

语种：英文

外文关键词：circle method; Diophantine equation; small prime solution

摘要：Let a(1), ..., a(6) be non-zero integers satisfying (a(i), a(j)) = 1, 1 <= i < j <= 6 and b be any integer. For the Diophantine equation a(1)p(1) + a(2)p(2)(3) + ... + a(6)p(6)(3) = b we prove that (i) if all a(1), ..., a(6) are positive and b >> max {vertical bar a(j)vertical bar}(34+epsilon), then the equation is soluble in primes p(j), and (ii) if a(1), ..., a(6) are not all of the same sign, then the equation has prime solutions satisfying max {p(1), p(2)(3), ..., p(6)(3)} << vertical bar b vertical bar + max {vertical bar a(j)vertical bar}(33+epsilon), where the implied constants depend only on epsilon.