On a binary additive problem involving fractional powers

被引：2

作者：

Yu, Gang ^{[1
]}

机构：

[1] Kent State Univ, Dept Math Sci, East Summit St, Kent, OH 45458 USA

来源：

JOURNAL OF NUMBER THEORY | 2020年 / 208卷

关键词：

Additive problem; Fractional powers; Exponential sums; van der Corput's method;

D O I：

10.1016/j.jnt.2019.07.019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that, for any given c is an element of (1, 11/10), every sufficiently large integer n can be represented as n = [m(c)] + [p(c)], where m is a positive integer and p is a prime, and [t] is the integer part of the real number t. We also prove that, when c is an element of (1, 1+root 5/2), such representation exists for almost all positive integers n. These respectively improve the results of A. Kumchev [9], and Balanzario, Garaev, and Zuazua [1]. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：101 / 119

页数：19

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