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...

Cur síos iomlán

Sonraí bibleagrafaíochta
Príomhchruthaitheoirí:	Ford, K, Green, B, Koukoulopoulos, D
Formáid:	Journal article
Teanga:	English
Foilsithe / Cruthaithe:	Springer 2023

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