From the 1 of 4 linked papers with an AI index.
4 papers
Fractal uncertainty principle over
Valentino Badalucco, Leonardo Franchi
The paper establishes a fractal uncertainty principle for porous subsets of the p‑adic field \(\mathbb{Q}_p\), confirming a conjecture posed by Cohen.
Product-free subsets of
Leonardo Franchi, W. T. Gowers, Fredy Yip
The third problem in Ben Green's collection of 100 open problems asks whether an open subset of that does not contain with must have measure at most 1/3. We…
A unified abstract regularity lemma
Gaia Carenini, Leonardo Franchi
The goal of this short note is to prove a unified abstract regularity lemma which recovers Szemerédi's graph regularity lemma, Green's arithmetic regularity lemma, and a regularit…
A strengthening of Chang's lemma
Gaia Carenini, Leonardo Franchi
We prove a strengthening of Chang's lemma for subsets of . The classical conclusion that the large spectrum is contained in a subspace of dimension at most $2\vareps…