Diophantine inequalities involving a prime and an almost-prime

Liyang Yang

doi:10.1016/j.jnt.2016.05.008

Diophantine inequalities involving a prime and an almost-prime

Liyang Yang

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that there are infinitely many solutions of|λ₀+λ₁p+λ₂P₃|<p⁻¹¹³¹, where λ₀ is an arbitrary real number and λ₁,λ₂∈R with λ₂≠0 and 0>λ1λ2 not in Q. This improves a result by Harman.

Original language	English (US)
Pages (from-to)	347-367
Number of pages	21
Journal	Journal of Number Theory
Volume	170
DOIs	https://doi.org/10.1016/j.jnt.2016.05.008
State	Published - Jan 1 2017
Externally published	Yes

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Keywords

Almost-primes
Diophantine inequalities
Sieve method

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10.1016/j.jnt.2016.05.008

Cite this

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title = "Diophantine inequalities involving a prime and an almost-prime",

abstract = "We prove that there are infinitely many solutions of|λ0+λ1p+λ2P3|−1131, where λ0 is an arbitrary real number and λ1,λ2∈R with λ2≠0 and 0>λ1λ2 not in Q. This improves a result by Harman.",

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AB - We prove that there are infinitely many solutions of|λ0+λ1p+λ2P3|−1131, where λ0 is an arbitrary real number and λ1,λ2∈R with λ2≠0 and 0>λ1λ2 not in Q. This improves a result by Harman.

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KW - Sieve method

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ER -

Diophantine inequalities involving a prime and an almost-prime

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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