RESEARCH ARTICLE

Diophantine inequalities over Piatetski-Shapiro primes

  • Jing HUANG 1 ,
  • Wenguang ZHAI 2 ,
  • Deyu ZHANG , 1
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  • 1. School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
  • 2. Department of Mathematics, China University of Mining and Technology, Beijing 100083, China

Received date: 25 Jun 2020

Accepted date: 28 Feb 2021

Published date: 15 Jun 2021

Copyright

2021 Higher Education Press

Abstract

Let c>1 and 0<γ<1: We study the solubility of the Diophantine inequality |p1c+p2c++pscN|<(logN)1 in Piatetski-Shapiro primes p1,p2, .., ps of the form pj=[mγ] for some m, and improve the previous results in the cases s = 2, 3, 4.

Cite this article

Jing HUANG , Wenguang ZHAI , Deyu ZHANG . Diophantine inequalities over Piatetski-Shapiro primes[J]. Frontiers of Mathematics in China, 2021 , 16(3) : 749 -770 . DOI: 10.1007/s11464-021-0916-7

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