On Diophantine approximation with one prime and three squares of primes

doi:10.1007/s11464-019-0776-6

Front. Math. China

2019, Vol. 14

Issue (4) : 761-779 https://doi.org/10.1007/s11464-019-0776-6

RESEARCH ARTICLE

On Diophantine approximation with one prime and three squares of primes

Wenxu GE¹(

), Feng ZHAO¹, Tianqin WANG²

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

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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 p_j, j =1, 2, 3, 4, to the inequality $| λ 1 p 1 + λ 2 p 22 + λ 3 p 32 + λ 4 p 42 y + w ‾ | < (max {p 1, p 22, p 32, p 42}) 5 / 64$ . This improves the earlier result.

Keywords Diophantine inequalities primes Davenport-Heilbronn method sieve methods

Corresponding Author(s): Wenxu GE

Issue Date: 23 September 2019

Cite this article:

Wenxu GE,Feng ZHAO,Tianqin WANG. On Diophantine approximation with one prime and three squares of primes[J]. Front. Math. China, 2019, 14(4): 761-779.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-019-0776-6
https://academic.hep.com.cn/fmc/EN/Y2019/V14/I4/761

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