A dichotomy in the tail behaviour of quadratic Weyl sums

Apparaît dans la collection : 2026 - T1 - WS3 - Integrating Research and Illustration in Number Theory

Jointly with Tariq Osman, we completed the classification of the tail behaviour of the limiting distributions of all quadratic Weyl sums of the form $1/\sqrt{N} \sum_{n=1}^N e( ((1/2)n^2+\beta n)x+\alpha n)$. When $\alpha$ and $\beta$ are both rational, while trying to understand the contribution of certain orbits to the heavy tails, we discovered that some pairs actually lead to a compactly supported limiting distribution. I will especially emphasise the role of mathematical illustration in our understanding of the geometry of the relevant orbits, as well the importance of numerical simulations to validate our results and prompt new questions.

Informations sur la vidéo

Date de captation 25/03/2026
Date de publication 20/05/2026
Institut IHP
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants, Etudiants
Réalisateur(s) Service audiovisuel de l'IHP
Format MP4
Lieu IHP - Hermite Amphitheater

Données de citation

DOI 10.57987/IHP.2026.T1.WS3.019
Citer cette vidéo Cellarosi, Francesco (25/03/2026). A dichotomy in the tail behaviour of quadratic Weyl sums. IHP. Audiovisual resource. DOI: 10.57987/IHP.2026.T1.WS3.019
URL https://dx.doi.org/10.57987/IHP.2026.T1.WS3.019

Domaine(s)

Théorie des nombres

Bibliographie

Heavy Tailed and Compactly Supported Distributions of Quadratic Weyl Sums with Rational Parameters (with Tariq Osman). To appear in Mathematische Annalen. arXiv: 2210.09838.