Diophantine Inequality by Unlike Powers of Primes

• 作者: Li ZHU
• 来源期刊: 数学年刊B辑（英文版）
• 年，卷（期）: 2022,（1）
• 页码范围: 125-136
• 页数: 12页
• 语种: 英文
• DOI: 10.1007/s11401-022-0326-5

摘要

Suppose that λ1,…,λ5 are nonzero real numbers,not all of the same sign,satisfying that λ1/λ2 is irrational.Then for any given real number η and ε ＞ 0,the inequality|λ1p1+λ2p22+λ3p33+λ4p44+λ5p55+η|＜(max1≤j≤5pjj)-19/756+ε has infinitely many solutions in prime variables p1,…,p5.This result constitutes an im-provement of the recent results.