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

共 50 条

[21] Arithmetic Progressions, Prime Numbers, and Squarefree Integers
Stuart Clary
Jacek Fabrykowski
[J]. Czechoslovak Mathematical Journal, 2004, 54 : 915 - 927
[22] On Integers for Which the Sum of Divisors is the Square of the Squarefree Core
Broughan, Kevin A.
De Koninck, Jean-Marie
Katai, Imre
Luca, Florian
[J]. JOURNAL OF INTEGER SEQUENCES, 2012, 15 (07)
[23] ON THE VARIANCE OF SQUAREFREE INTEGERS IN SHORT INTERVALS AND ARITHMETIC PROGRESSIONS
Gorodetsky, Ofir
Matomaki, Kaisa
Radziwill, Maksym
Rodgers, Brad
[J]. GEOMETRIC AND FUNCTIONAL ANALYSIS, 2021, 31 (01) : 111 - 149
[24] On the variance of squarefree integers in short intervals and arithmetic progressions
Ofir Gorodetsky
Kaisa Matomäki
Maksym Radziwiłł
Brad Rodgers
[J]. Geometric and Functional Analysis, 2021, 31 : 111 - 149
[25] The Erdos discrepancy problem over the squarefree and cubefree integers
Aymone, Marco
[J]. MATHEMATIKA, 2022, 68 (01) : 51 - 73
[26] Explicit bounds for separation between Oseledets subspaces
Quas, Anthony
Thieullen, Philippe
Zarrabi, Mohamed
[J]. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2019, 34 (03): : 517 - 560
[27] Distribution of nonlinear congruential pseudorandom numbers modulo almost squarefree integers
El-Mahassni, Edwin D.
Shparlinski, Igor E.
Winterhof, Arne
[J]. MONATSHEFTE FUR MATHEMATIK, 2006, 148 (04): : 297 - 307
[28] ON SETS OF INTEGERS WITH PRESCRIBED GAPS
STADJE, W
[J]. ADVANCES IN APPLIED PROBABILITY, 1992, 24 (04) : 776 - 777
[29] ON SETS OF INTEGERS WITH PRESCRIBED GAPS
BARYSHNIKOV, Y
STADJE, W
[J]. MONATSHEFTE FUR MATHEMATIK, 1993, 116 (02): : 83 - 98
[30] On Fourier coefficients of modular forms of half integral weight at squarefree integers
Y.-J. Jiang
Y.-K. Lau
G.-S. Lü
E. Royer
J. Wu
[J]. Mathematische Zeitschrift, 2019, 293 : 789 - 808

← 1 2 3 4 5 →