Diophantine approximation over Piatetski-Shapiro primes

JOURNAL OF NUMBER THEORY

卷:211

Article

Li, Taiyu¹  Liu, Huafeng² 

[1] Shandong Univ Weihai, Sch Math & Stat, 180 Wenhua Xilu, Weihai 264209, Shandong, Peoples R China

[2] Shandong Normal Univ, Sch Math & Stat, 88 Wenhua Donglu, Jinan 250014, Shandong, Peoples R China

关键词: Diophantine inequalities;    Piatetski-Shapiro primes;    Additive problems;    Exponential sums;   

DOI  :  10.1016/j.jnt.2019.10.002

来源: Elsevier

【 摘 要 】

Let c > 1 and 0 < gamma < 1 he real. In this paper, we study the solubility of the Diophantine inequality vertical bar P-1(c) + P-2(c) + center dot center dot center dot + p(s)(c) - N vertical bar < epsilon in Piatetski-Shapiro primes p(1), p(2), ... ,p(s) of the form p(j) = [m(1/gamma)] for some m epsilon N, and improve the previous results of Kumchev and Petrov [20]. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free