A structure theorem for sets of small popular doubling

• Autorzy: Przemysław Mazur
• Języki publikacji: EN

Abstrakty

EN

We prove that every set A ⊂ ℤ satisfying $∑_{x}min(1_A*1_A(x),t) ≤ (2+δ)t|A|$ for t and δ in suitable ranges must be very close to an arithmetic progression. We use this result to improve the estimates of Green and Morris for the probability that a random subset A ⊂ ℕ satisfies |ℕ∖(A+A)| ≥ k; specifically, we show that $ℙ(|ℕ∖(A+A)| ≥ k) = Θ(2^{-k/2})$.

Kategorie tematyczne

• 11P70: Inverse problems of additive number theory, including sumsets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 171
• Numer: 3
• Strony: 221-239

Daty

wydano

2015

Twórcy

autor

Przemysław Mazur

• Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, United Kingdom

Identyfikatory

DOI

10.4064/aa171-3-2