The estimate for mean values on prime numbers relative to frac{4}{p} = frac{1}{{n_1 }} + frac{1}{{n_2 }} + frac{1}{{n_3 }} |
| |
| Authors: | ChaoHua Jia |
| |
| Affiliation: | 1. Institute of Mathematics, Chinese Academy of Sciences, Beijing, 100190, China
2. Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing, 100190, China
|
| |
| Abstract: | If n is a positive integer, let f(n) denote the number of positive integer solutions (n 1, n 2, n 3) of the Diophantine equation $frac{4} {n} = frac{1} {{n_1 }} + frac{1} {{n_2 }} + frac{1} {{n_3 }} $ For the prime number p, f(p) can be split into f 1(p) + f 2(p), where f i (p) (i = 1, 2) counts those solutions with exactly i of denominators n 1, n 2, n 3 divisible by p. In this paper, we shall study the estimate for mean values $sumlimits_{p < x} {f_i (p),i = 1,2,} $ , where p denotes the prime number. |
| |
| Keywords: | Diophantine equation prime number mean value |
| 本文献已被 CNKI SpringerLink 等数据库收录！ |
|
