A system of two Diophantine inequalities with primes
type: Item
instance of: scholarly article
title: A system of two Diophantine inequalities with primes
zbMATH Open document ID: 1477.11175
DOI: 10.1155/2021/6613947
author: Xue Han
author: Huafeng Liu
author: Deyu Zhang
published in: Journal of Mathematics
publication date: 2021-06-23T00:00:00Z
review text: Summary: Let \(1<d<c<128/119\), \(1<\alpha <\beta< 6^{1-d/c}\). In this paper, we prove that there exist positive real numbers \(N_1^{(0)}\) and \(N_2^{(0)}\) depending on \(c\), \(d\), \(\alpha\), \(\beta\) such that for all real numbers \(N_1>N_1^{(0)}\), \(N_2>N_2^{(0)}\) and \(\alpha\leq N_2/N_1^{d / c}\leq\beta\), the system of two Diophantine inequalities \(|p_1^c + \cdots + p_6^c - N_1|<N_1^{-(1/c) (128/119-c)} \log^{109} N_1,| p_1^d + \cdots + p_6^d - N_2|<N_2^{-(1/d) (128/119-d)} \log^{109} N_2\) is solvable in prime variables \(p_1,\dots, p_6\).
Mathematics Subject Classification ID: 11P32
Mathematics Subject Classification ID: 11J25
Mathematics Subject Classification ID: 11P05
zbMATH DE Number: 7362411
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/6613947
OpenAlex ID: W3131412916
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description: scientific article; zbMATH DE number 7362411