An additive equation involving fractional powers

被引：2
|
作者：
Zhu, L. [1 ]
机构：
[1] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China
来源：
ACTA MATHEMATICA HUNGARICA | 2019年 / 159卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Diophantine equation; exponential sum; prime;
D O I：
10.1007/s10474-019-00979-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let 1 < c < 14/11 and N be a sufficiently large integer. We prove that almost all n is an element of (N, 2N] can be represented as n = [p(1)(c)] + [p(2)(c)], where p(1), p(2) are prime numbers and [x] denotes the integer part of x. Our method also yields an asymptotic formula for the number of representations of these n. The range 1 < c < 14/11 constitutes an extension of 1 < c < 17/16 due to Laporta.
引用
收藏
页码：174 / 186
页数：13
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