Diophantine inequalities over Piatetski-Shapiro primes期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Diophantine inequalities over Piatetski-Shapiro primes

Authors:	Jing HUANG Wenguang ZHAI Deyu ZHANG

Affiliation:	¹. School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China². Department of Mathematics, China University of Mining and Technology, Beijing 100083, China

Abstract:	Let c>1 and $0 < γ < 1$ : We study the solubility of the Diophantine inequality $\| p 1 c + p 2 c + ⋯ + p s c − N \| < (l o g N) − 1$ in Piatetski-Shapiro primes p₁,p₂, .., p_s of the form $p j = [m γ]$ for some $m ∈ ℕ$ , and improve the previous results in the cases s = 2, 3, 4.

Keywords:	Diophantine inequalities Piatetski-Shapiro primes exponential sums additive problems

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