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| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Kevin, Ford | - |
| dc.contributor.author | Ben, Green | - |
| dc.contributor.author | Dimitris, Koukoulopoulos | - |
| dc.date.accessioned | 2023-04-04T07:17:39Z | - |
| dc.date.available | 2023-04-04T07:17:39Z | - |
| dc.date.issued | 2023 | - |
| dc.identifier.uri | https://link.springer.com/article/10.1007/s00222-022-01177-y | - |
| dc.identifier.uri | https://dlib.phenikaa-uni.edu.vn/handle/PNK/7492 | - |
| dc.description | CC BY | vi |
| dc.description.abstract | 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. | vi |
| dc.language.iso | en | vi |
| dc.publisher | Springer | vi |
| dc.subject | defining Δ(n):=maxt#{d|n,logd∈[t,t+1]} | vi |
| dc.subject | Δ(n)⩾(loglogn)0.35332277… for almost all n | vi |
| dc.title | Equal sums in random sets and the concentration of divisors | vi |
| dc.type | Book | vi |
| Appears in Collections | ||
| OER - Khoa học Tự nhiên | ||
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