Estimation of Exponential Sums over Primes in Short Intervals I |
| |
| Authors: | Jianya Liu Tao Zhan |
| |
| Institution: | (1) Department of Mathematics, Shandong University, 250100 Jinan, P.R. China, e-mail: zhantao@sdu.edu.cn, CN |
| |
| Abstract: | Let and be the von Mangoldt function and M?bius function, respectively, x real and y“small” compared with x. This paper gives, for the first time, a non-trivial estimate of the sum
for all whenever . Correspondingly, it is also proved that
uniformly for all real α and any , and in the same range of y.
Received 10 December 1996; in revised form 9 September 1997 |
| |
| Keywords: | : Exponential sums von Mangoldt function short intervals |
| 本文献已被 SpringerLink 等数据库收录！ |
|
