Values of binary linear forms at prime arguments

doi:10.1007/s11464-015-0461-3

Front. Math. China

2015, Vol. 10

Issue (6) : 1449-1459 https://doi.org/10.1007/s11464-015-0461-3

RESEARCH ARTICLE

Values of binary linear forms at prime arguments

Yuchao WANG(

)

Department of Mathematics, Shanghai University, Shanghai 200444, China

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Abstract

value of a given binary linear form at prime arguments. Let λ₁ and λ₂ be positive real numbers such that λ₁/λ₂ is irrational and algebraic. For any (C, c) well-spaced sequence V and δ>0, let E(V, X, δ) denote the number of υ∈V with υ≤X for which the inequality

|λ1p1+λ2ρ2−υ|<υ−δ

has no solution in primes p₁, p₂. It is shown that for any ε>0,we have E(V, X, δ) «max(X35+2δ+ε,X23+43δ+ε).

Keywords Circle method Diophantine inequality

Corresponding Author(s): Yuchao WANG

Issue Date: 12 October 2015

Cite this article:

Yuchao WANG. Values of binary linear forms at prime arguments[J]. Front. Math. China, 2015, 10(6): 1449-1459.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-015-0461-3
https://academic.hep.com.cn/fmc/EN/Y2015/V10/I6/1449

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