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Updated Oct 8

Problem 40

Statement. For what functions $g(N)\to \infty$ is it true that

\lvert A\cap \{1,\ldots,N\}\rvert \gg \frac{N^{1/2}}{g(N)}

implies $\limsup 1_A\ast 1_A(n)=\infty$ ?

Status. Open.

Source. erdosproblems.com/40, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #40, https://www.erdosproblems.com/40.

Formalization. Statement in formal-conjectures.

Progress

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Known Results

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Linked library material

These entries are derived from explicit links on library pages. They are navigation only and do not by themselves record mathematical progress.

Linked from (4)

Additive Bases and Sidon Sets Additive Bases and Sidon Sets additive_combinatorics/erdos_1956_problems_results_additive_number_theory Conjecture (p. 128): the Erdős–Turán conjecture and the stronger conjecture under a_k < ck^2

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