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Equal sums in random sets and the concentration of divisors

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Main Authors: Kevin, Ford, Ben, Green, Dimitris, Koukoulopoulos
Format: Book
Language:English
Published: Springer 2023
Subjects:
defining Δ(n):=maxt#{d|n,logd∈[t,t+1]}
Δ(n)⩾(loglogn)0.35332277… for almost all n
Online Access:https://link.springer.com/article/10.1007/s00222-022-01177-y
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7492
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spelling oai:localhost:PNK-74922023-04-04T07:17:39Z Equal sums in random sets and the concentration of divisors Kevin, Ford Ben, Green Dimitris, Koukoulopoulos defining Δ(n):=maxt#{d|n,logd∈[t,t+1]} Δ(n)⩾(loglogn)0.35332277… for almost all n CC BY We study the extent to which divisors of a typical integer n are concentrated. In particular, defining Δ(n):=maxt#{d|n,logd∈[t,t+1]}, we show that Δ(n)⩾(loglogn)0.35332277… for almost all n, a bound we believe to be sharp. This disproves a conjecture of Maier and Tenenbaum. We also prove analogs for the concentration of divisors of a random permutation and of a random polynomial over a finite field. Most of the paper is devoted to a study of the following much more combinatorial problem of independent interest. 2023-04-04T07:17:39Z 2023-04-04T07:17:39Z 2023 Book https://link.springer.com/article/10.1007/s00222-022-01177-y https://dlib.phenikaa-uni.edu.vn/handle/PNK/7492 en application/pdf Springer
institution Digital Phenikaa
collection Digital Phenikaa
language English
topic defining Δ(n):=maxt#{d|n,logd∈[t,t+1]}
Δ(n)⩾(loglogn)0.35332277… for almost all n
spellingShingle defining Δ(n):=maxt#{d|n,logd∈[t,t+1]}
Δ(n)⩾(loglogn)0.35332277… for almost all n
Kevin, Ford
Ben, Green
Dimitris, Koukoulopoulos
Equal sums in random sets and the concentration of divisors
description CC BY
format Book
author Kevin, Ford
Ben, Green
Dimitris, Koukoulopoulos
author_facet Kevin, Ford
Ben, Green
Dimitris, Koukoulopoulos
author_sort Kevin, Ford
title Equal sums in random sets and the concentration of divisors
title_short Equal sums in random sets and the concentration of divisors
title_full Equal sums in random sets and the concentration of divisors
title_fullStr Equal sums in random sets and the concentration of divisors
title_full_unstemmed Equal sums in random sets and the concentration of divisors
title_sort equal sums in random sets and the concentration of divisors
publisher Springer
publishDate 2023
url https://link.springer.com/article/10.1007/s00222-022-01177-y
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7492
_version_ 1762274899592740864
score 8.891053

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