两个素数和一个素数平方和的丢番图逼近

数学季刊 ›› 2012, Vol. 27 ›› Issue (3): 417-423.

两个素数和一个素数平方和的丢番图逼近

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

收稿日期:2011-01-10 出版日期:2012-09-30 发布日期:2023-03-24
作者简介: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.
基金资助:
Supported by the NNSF of China(11071070); Supported by the Science Research Plan of Education Department of Henan Province(2011B110002)

Diophantine Approximation with Two Primes and One Square of Prime

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)

摘要/Abstract

摘要： We show that if λ₁, λ₂, λ₃ are non-zero real numbers, not all of the same sign, η is real and λ₁/λ₂ is irrational, then there are infinitely many ordered triples of primes (p₁, p₂, p₃) for which |λ₁p₁+λ₂p₂+λ₃p²₃₊η| < (maxp_j )- 1/40 (logmaxp_j)⁴.

关键词: Diophantine approximation, prime, Davenport-Heilbronn method

Abstract: We show that if λ₁, λ₂, λ₃ are non-zero real numbers, not all of the same sign, η is real and λ₁/λ₂ is irrational, then there are infinitely many ordered triples of primes (p₁, p₂, p₃) for which |λ₁p₁+λ₂p₂+λ₃p²₃₊η| < (maxp_j )- 1/40 (logmaxp_j)⁴.

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

中图分类号:

O156.4

李伟平, 王天泽. 两个素数和一个素数平方和的丢番图逼近[J]. 数学季刊, 2012, 27(3): 417-423.

LI Wei-ping, WANG Tian-ze. Diophantine Approximation with Two Primes and One Square of Prime[J]. Chinese Quarterly Journal of Mathematics, 2012, 27(3): 417-423.

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