RESEARCH ARTICLE

On Diophantine approximation with one prime and three squares of primes

  • Wenxu GE , 1 ,
  • Feng ZHAO 1 ,
  • Tianqin WANG 2
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  • 1. School of Mathematics Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046, China
  • 2. School of Information Engineering, North China University of Water Resources and Electric Power, Zhengzhou 450046, China

Received date: 17 Dec 2018

Accepted date: 18 Jun 2019

Published date: 15 Aug 2019

Copyright

2019 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature

Abstract

Let λ1, λ2, λ3, λ4 be non-zero real numbers, not all of the same sign, w real. Suppose that the ratios λ1/λ2, λ1/λ3 are irrational and algebraic. Then there are in.nitely many solutions in primes pj, j =1, 2, 3, 4, to the inequality |λ1p1+ λ2p22+λ3p32+λ4p42y+w|<(max{p1,p22,p32,p42})5/64. This improves the earlier result.

Cite this article

Wenxu GE , Feng ZHAO , Tianqin WANG . On Diophantine approximation with one prime and three squares of primes[J]. Frontiers of Mathematics in China, 2019 , 14(4) : 761 -779 . DOI: 10.1007/s11464-019-0776-6

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