Diophantine Inequality by Unlike Powers of Primes

被引：2

作者：

ZHU, Li ^{[1
]}

机构：

[1] Shanghai Lixin Univ Accounting & Finance, Sch Math & Stat, Shanghai 201209, Peoples R China

来源：

CHINESE ANNALS OF MATHEMATICS SERIES B | 2022年 / 43卷 / 01期

关键词：

Prime; Davenport-Heilbronn method; Diophantine inequalities; 3; SQUARES; APPROXIMATION; VALUES; FORMS; SUMS;

D O I：

10.1007/s11401-022-0326-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Suppose that lambda(1), ..., lambda(5) are nonzero real numbers, not all of the same sign, satisfying that lambda(1)/lambda(2) is irrational. Then for any given real number eta and epsilon > 0, the inequality vertical bar lambda(1)p(1) + lambda(2)p(2)(2) + lambda(3)p(3)(3 )+ lambda(4)p(4)(4) + lambda(5)p(5)(5) + eta vertical bar < (max(1 <= j <= 5) p(j)(j))(-19/756+epsilon) has infinitely many solutions in prime variables p(1), ..., p(5). This result constitutes an improvement of the recent results.

引用

页码：125 / 136

页数：12

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