Equal sums in random sets and the concentration of divisors

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...

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Autori principali:	Ford, K, Green, B, Koukoulopoulos, D
Natura:	Journal article
Lingua:	English
Pubblicazione:	Springer 2023

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