{"title":"关于有特殊类型素数 II 的三元二叉不等式","authors":"Li Zhu","doi":"10.1007/s10998-024-00602-4","DOIUrl":null,"url":null,"abstract":"<p>Suppose that <i>N</i> is a sufficiently large real number and <i>E</i> is an arbitrarily large constant. In this paper, it is proved that, for <span>\\(1< c < \\frac{7}{6}\\)</span>, the Diophantine inequality </p><span>$$\\begin{aligned} |p_1^c+p_2^c+p_3^c-N|<(\\log N)^{-E} \\end{aligned}$$</span><p>is solvable in prime variables <span>\\(p_1,p_2,p_3\\)</span> so that each of the numbers <span>\\(p_i+2,\\,i=1,2,3\\)</span>, has at most <span>\\(\\big [3.43655+{\\frac{12.12}{7-6c}}\\big ]\\)</span> prime factors counted with multiplicity.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On a ternary diophantine inequality with prime numbers of a special type II\",\"authors\":\"Li Zhu\",\"doi\":\"10.1007/s10998-024-00602-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Suppose that <i>N</i> is a sufficiently large real number and <i>E</i> is an arbitrarily large constant. In this paper, it is proved that, for <span>\\\\(1< c < \\\\frac{7}{6}\\\\)</span>, the Diophantine inequality </p><span>$$\\\\begin{aligned} |p_1^c+p_2^c+p_3^c-N|<(\\\\log N)^{-E} \\\\end{aligned}$$</span><p>is solvable in prime variables <span>\\\\(p_1,p_2,p_3\\\\)</span> so that each of the numbers <span>\\\\(p_i+2,\\\\,i=1,2,3\\\\)</span>, has at most <span>\\\\(\\\\big [3.43655+{\\\\frac{12.12}{7-6c}}\\\\big ]\\\\)</span> prime factors counted with multiplicity.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-07-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10998-024-00602-4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10998-024-00602-4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
假设 N 是一个足够大的实数，E 是一个任意大的常数。本文证明，对于 \(1< c < \frac{7}{6}\), Diophantine 不等式 $$\begin{aligned}.|p_1^c+p_2^c+p_3^c-N|<(\log N)^{-E}\end{aligned}$$在素数变量 \(p_1,p_2,p_3\)中是可解的，因此每个数 \(p_i+2,\,i=1,2,3\)，最多有\(\big [3.43655+{frac{12.12}{7-6c}}\big ]\)以倍数计算的素因子。
On a ternary diophantine inequality with prime numbers of a special type II
Suppose that N is a sufficiently large real number and E is an arbitrarily large constant. In this paper, it is proved that, for \(1< c < \frac{7}{6}\), the Diophantine inequality
is solvable in prime variables \(p_1,p_2,p_3\) so that each of the numbers \(p_i+2,\,i=1,2,3\), has at most \(\big [3.43655+{\frac{12.12}{7-6c}}\big ]\) prime factors counted with multiplicity.
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