Equal sums in random sets and the concentration of divisors
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...
Prif Awduron: | Ford, K, Green, B, Koukoulopoulos, D |
---|---|
Fformat: | Journal article |
Iaith: | English |
Cyhoeddwyd: |
Springer
2023
|
Eitemau Tebyg
-
On a Sum Involving the Sum-of-Divisors Function
gan: Feng Zhao, et al.
Cyhoeddwyd: (2021-01-01) -
On the sum of positive divisors functions
gan: Erban, R, et al.
Cyhoeddwyd: (2021) -
On the divisor sums in arithmetical progressions
gan: Eugenijus Stankus
Cyhoeddwyd: (1998-12-01) -
A Paradigmatic Approach to Find Equal Sum Partitions of Zero-Divisors via Complete Graphs
gan: M. Haris Mateen, et al.
Cyhoeddwyd: (2022-01-01) -
Moments of zeta and correlations of divisor-sums: V
gan: Conrey, B, et al.
Cyhoeddwyd: (2018)