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The Ramanujan Journal

, Volume 25, Issue 3, pp 343–357 | Cite as

Diophantine approximation with one prime and three squares of primes

  • Weiping Li
  • Tianze Wang
Article

Abstract

We show that if λ 1,λ 2,λ 3,λ 4 are nonzero real numbers, not all of the same sign, η is real, and at least one of the ratios λ 1/λ j (j=2,3,4) is irrational, then given any real number ω>0, there are infinitely many ordered quadruples of primes (p 1,p 2,p 3,p 4) for which
$$\bigl|\lambda_1 p_1+\lambda_2 p^2_2+\lambda_3 p^2_3+\lambda_4p^2_4+\eta \bigr|<(\max p_j)^{-\frac{1}{28}+\omega}.$$

Keywords

Diophantine approximation Prime Davenport–Heilbronn method 

Mathematics Subject Classification (2010)

11D75 11P32 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mathematics and Information ScienceHenan University of Finance and EconomicsZhengzhouP.R. China
  2. 2.School of Mathematics and Information ScienceNorth China University of Water Conservancy and Electric PowerZhengzhouP.R. China

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