11 citations · 13 across the 7 of their papers we have counts for
7 papers
A note on iterated sumsets races
Paul Péringuey, Anne de Roton
This short note answers a question raised by Nathanson \cite{Nath25} about "races" between iterated sumsets. We prove that for any integer , there are finite sets of integers $A…
Additively stable sets, critical sets for the 3k-4 theorem in and
Paul Péringuey, Anne de Roton
We describe in this paper additively left stable sets, i.e. sets satisfying (meaning that is stable by addition with…
Small sumsets in real line : a continuous 3k-4 theorem
Anne de Roton
We prove a continuous Freiman's theorem for small sumsets in by using some ideas from Ruzsa's work on measure of sumsets in as well as some graphic…
Maximal sets with no solution to x+y=3z
Alain Plagne, Anne de Roton
In this paper, we are interested in a generalization of the notion of sum-free sets. We address a conjecture first made in the 90s by Chung and Goldwasser. Recently, after some com…
Generalization of the effective Wiener-Ikehara theorem
Szilárd Gy. Révész, Anne de Roton
We consider the classical Wiener-Ikehara Tauberian theorem, with a generalized condition of slow decrease and some additional poles on the boundary of convergence of the Laplace tr…
Improving Roth's theorem in the primes
Harald Andres Helfgott, Anne de Roton
Let A be a subset of the primes. Let δ_P(N) = \frac{|\{n\in A: n\leq N\}|}{|\{\text{ prime}: n\leq N\}|}. We prove that, if δ_P(N)\geq C \frac{\log \log \log N}{(\log \log N)^{1…