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A quaternary Diophantine inequality with prime numbers of a special form (II)
Abstract
Let N be a sufficiently large real number. In this paper, it is proved that, for 1<c<5179/3909 and for any arbitrary large number E>0, the Diophantine inequality |p1c+p2c+p3c+p4c−N|<(log N)−E is solvable in prime variables p1,p2,p3,p4 such that each of the numbers pi+2 (i=1,2,3,4) has, counted according to multiplicity, at most [31250/(5179−3909c)] prime factors, which constitutes a large improvement upon the previous results of Dimitrov [13] and Li-Xue-Zhang [22], respectively.
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BibTeX
@misc{zhao2026quaternary,
title = {{A quaternary Diophantine inequality with prime numbers of a special form (II)}},
author = {Yuhua Zhao and Jinjiang Li and Linji Long and Min Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28774},
eprint = {2610.28774},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28774},
}
RIS
TY - UNPB
TI - A quaternary Diophantine inequality with prime numbers of a special form (II)
AU - Yuhua Zhao
AU - Jinjiang Li
AU - Linji Long
AU - Min Zhang
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28774
UR - https://arxiv.org/abs/2610.28774
AB - Let N be a sufficiently large real number. In this paper, it is proved that, for 1<c<5179/3909 and for any arbitrary large number E>0, the Diophantine inequality |p_1^c+p_2^c+p_3^c+p_4^c−N|<(log N)^−E is solvable in prime variables p_1,p_2,p_3,p_4 such that each of the numbers p_i+2 (i=1,2,3,4) has, counted according to multiplicity, at most [31250/(5179−3909c)] prime factors, which constitutes a large improvement upon the previous results of Dimitrov [13] and Li-Xue-Zhang [22], respectively.
ER -