Explicit bounds for large gaps between squarefree integers

被引：1

作者：

Kumchev, Angel ^{[1
]}

Mccormick, Wade ^{[2
]}

Mcnew, Nathan ^{[1
]}

Park, Ariana ^{[3
]}

Scherr, Russell ^{[1
]}

Ziehr, Willow ^{[2
]}

机构：

[1] Towson Univ, Dept Math, Towson, MD 21252 USA

[2] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

[3] MIT, Dept Math, Cambridge, MA 02139 USA

来源：

JOURNAL OF NUMBER THEORY | 2024年 / 254卷

基金：

美国国家科学基金会;

关键词：

Squarefree integers; Gaps; Explicit bounds; POWER FREE VALUES;

D O I：

10.1016/j.jnt.2023.07.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain explicit forms of the current best known asymptotic upper bounds for gaps between squarefree integers. In particular we show, for any x & GE; 2, that every interval of the form (x, x + 11x1/5 log x] contains a squarefree integer. The constant 11 can be improved further, if x is assumed to be larger than a (very) large constant.& COPY; 2023 Elsevier Inc. All rights reserved.

引用

页码：336 / 357

页数：22

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