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...
| Main Authors: | , , |
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| Formato: | Journal article |
| Idioma: | English |
| Publicado: |
Springer
2023
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