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Bibliographic Details
Main Author: Weingartner, Andreas
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2604.22058
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author Weingartner, Andreas
author_facet Weingartner, Andreas
contents We establish a relationship between error terms appearing in estimates for the counting functions of smooth and rough numbers. We then apply this link to obtain an explicit upper bound for the error term in de Bruijn's approximation $Λ$ for the count of smooth numbers, from an explicit upper bound, due to Fan, for the error term in a variant of de Bruijn's estimate for the count of rough numbers.
format Preprint
id arxiv_https___arxiv_org_abs_2604_22058
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A link between error terms when counting smooth and rough numbers
Weingartner, Andreas
Number Theory
11N25
We establish a relationship between error terms appearing in estimates for the counting functions of smooth and rough numbers. We then apply this link to obtain an explicit upper bound for the error term in de Bruijn's approximation $Λ$ for the count of smooth numbers, from an explicit upper bound, due to Fan, for the error term in a variant of de Bruijn's estimate for the count of rough numbers.
title A link between error terms when counting smooth and rough numbers
topic Number Theory
11N25
url https://arxiv.org/abs/2604.22058