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

页码：174 / 186

页数：13

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