Equal sums in random sets and the concentration of divisors
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| Định dạng: | Sách |
| Ngôn ngữ: | English |
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Springer
2023
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| Truy cập trực tuyến: | https://link.springer.com/article/10.1007/s00222-022-01177-y https://dlib.phenikaa-uni.edu.vn/handle/PNK/7492 |
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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 |
8.891145 |