OPENNOTORIOUSnumber theorySidon setsadditive combinatorics
Is there an infinite Sidon set $A\subset \mathbb{N}$ such that $|A\cap \{1,\ldots,N\}| \gg_\epsilon N^{1/2-\epsilon}$ for all $\epsilon>0$?
Notes: Best bound is >> N^{sqrt(2)-1+o(1)} by Ruzsa. Erdos proved any infinite Sidon set must satisfy liminf |A cap {1,...,N}| / N^{1/2} = 0.
AI Status: NONE · 0 total attempts