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The solubility of certain diophantine inequalities

Authors:	Hongze Li

Institution:	(1) Department of Mathematics, Shandong University, 250100 Ji'nan, People's Republic of China

Abstract:	Let ₁, ₂, ..., _s bes non-zero real numbers not all of the same sign and not all in rational ratio, andk be a natural number; letD(k) be the leasts for which the inequality $\left\| {\eta + \sum\nolimits_{j = 1}^s {\lambda _j n_j^k } } \right\|$ < (maxn _j)^– has infinitely many solutions. In this paper, we give some new estimations ofD(k) fork 6.Supported by the National Natural Science Foundation of China

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