The pointwise behavior of Riemann's function

Orateur: Jasson VINDAS
Localisation: Université de Gand, Belgique
Type: Séminaire cristolien d'analyse multifractale
Site: UPEC
Salle: BM 105
Date de début: 24/11/2022 - 15:00
Date de fin: 24/11/2022 - 16:00

In this talk we will present a new and simple method for the determination of the pointwise Hölderexponent of Riemann’s function ∞∑n=1sin(πn2x)n2 at every point of the real line. In contrast to other approaches, where wavelet analysis and the theta modular group were needed for the analysis of irrational points, our method is direct and elementary, being only based on the following tools from number theory and complex analysis: the evaluation of quadratic Gauss sums, the Poisson summation formula, and Cauchy’s theorem.The talk is based on collaborative work with Frederik Broucke.