Small prime solutions of a pair of linear equations in five prime variables |
| |
| Authors: | Zhen Cui Hong Ze Li |
| |
| Institution: | (1) Department of Mathematics, Shanghai Jiaotong University, Shanghai 200030, P. R. China;(2) Department of Mathematics and Statistics, University of Regina, Regina, SK S4S 0A2, Canada |
| |
| Abstract: | Assume an additional congruent condition on the coefficients. We prove that the pair of linear equations Σ
j=15
a
λj
p
j
= b
λ
(λ = 1, 2) has solutions in primes p
j
satisfying p
j
≪ |b
1| + |b2| +1)max
λ,j
|a
λj
|2318+ɛ
. This improves the exponent 79680 without assuming the additional condition of the second author’s. |
| |
| Keywords: | Diophantine equations Deuring-Heilbronn phenomenon large sieve inequality zero-free region |
| 本文献已被 维普 SpringerLink 等数据库收录！ |
|
