TY - JOUR
AU - Zhu, Li
AB - Suppose that λ1, ⋯ λ5 are nonzero real numbers, not all of the same sign, satisfying that λ1λ2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{{\lambda _1}} \over {{\lambda _2}}}$$\end{document} is irrational. Then for any given real number η and ε > 0, the inequality|λ1p1+λ2p22+λ3p33+λ4p44+λ5p55+η|<(max1≤j≤5pjj)−19756+ε\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\left| {{\lambda _1}{p_1} + {\lambda _2}p_2^2 + {\lambda _3}p_3^3 + {\lambda _4}p_4^4 + {\lambda _5}p_5^5 + \eta } \right| < {\left( {\mathop {\max }\limits_{1 \le j \le 5} p_j^j} \right)^{ - {{19} \over {756}} + \varepsilon }}$$\end{document}has infinitely many solutions in prime variables p1, ⋯, p5. This result constitutes an improvement of the recent results.
TI - Diophantine Inequality by Unlike Powers of Primes
JF - "Chinese Annals of Mathematics, Series B"
DO - 10.1007/s11401-022-0326-5
DA - 2022-01-01
UR - https://www.deepdyve.com/lp/springer-journals/diophantine-inequality-by-unlike-powers-of-primes-H0T1Z9IBbt
SP - 125
EP - 136
VL - 43
IS - 1
DP - DeepDyve
ER -