期刊论文详细信息
JOURNAL OF NUMBER THEORY 卷:192
The values of binary linear forms at prime arguments
Article
Ge, Wenxu1  Zhang, Min2  Li, Jinjiang2 
[1] North China Univ Water Resources & Elect Power, Sch Math Stat, Zhengzhou 450046, Henan, Peoples R China
[2] China Univ Min & Technol, Dept Math, Beijing 100083, Peoples R China
关键词: Diophantine inequalities;    Primes;    Davernport-Heilbronn method;   
DOI  :  10.1016/j.jnt.2018.03.016
来源: Elsevier
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【 摘 要 】

Suppose that lambda(1) and lambda(2) are positive real numbers such that lambda(1)/lambda(2 )is irrational and algebraic. Let V be a well-spaced sequence and delta > 0. Denote by E(V, X, delta) the number of v is an element of V with v <= X such that the inequality vertical bar lambda(1)p(1)+ lambda(2)p(2) - v vertical bar < v(-delta) has no solution in primes p(1), p(2). We prove that for all X >= 1, E(V, X, delta) << X f((delta)+epsilon) for any epsilon > 0 with f(delta) = max(5/9 + 2 delta, 2/3 + 4 delta/3), which improves the earlier result. (C) 2018 Elsevier Inc. All rights reserved.

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