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 | |
【 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.
【 授权许可】
Free
【 预 览 】
Files | Size | Format | View |
---|---|---|---|
10_1016_j_jnt_2018_03_016.pdf | 287KB | download |