Chinese Quarterly Journal of Mathematics ›› 2012, Vol. 27 ›› Issue (3): 417-423.

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Diophantine Approximation with Two Primes and One Square of Prime

  

  1. 1. Department of Mathematics and Information Science, Henan University of Economics and Law 2. School of Mathematics and Information Science, North China University of Water Conservancy and Electric Power

  • Received:2011-01-10 Online:2012-09-30 Published:2023-03-24
  • About author:LI Wei-ping(1972-), male, native of Zhoukou, Henan, an associate professor of Henan University of Economics and Law, Ph.D., engages in analytic number theory.
  • Supported by:
    Supported by the NNSF of China(11071070); Supported by the Science Research Plan of Education Department of Henan Province(2011B110002)

Abstract: We show that if λ1, λ2, λ3 are non-zero real numbers, not all of the same sign, η is real and λ12 is irrational, then there are infinitely many ordered triples of primes (p1, p2, p3) for which |λ1p12p23p23+η| < (maxpj )- 1/40 (logmaxpj)4.

Key words: Diophantine approximation, prime, Davenport-Heilbronn method

CLC Number: