# Séminaires : Séminaire Théorie des Nombres

 Equipe(s) : fa, tn, tga, Responsables : Marc Hindry, Bruno Kahn, Wieslawa Niziol, Cathy Swaenepoel Email des responsables : cathy.swaenepoel@imj-prg.fr Salle : Adresse : Description http://www.imj-prg.fr/tn/STN/stnj.html

 Orateur(s) Igor Shparlinski - University of New South Wales, Titre Maximal Operators and Restriction Bounds for Weyl Sums Date 20/06/2022 Horaire 14:00 à 15:00 Diffusion Résume We describe several recent results on so called maximal operators on Weyl sums $$S(u;N) =\sum_{1\le n \le N} \exp(2 \pi i (u_1n+…+u_dn^d)),$$ where $u = (u_1,...,u_d) \in [0,1)^d$. Namely, given a partition $I \cup J \subseteq \{1,…,d\}$, we define the map $$(u_i)_{i \in I} \mapsto \sup_{u_j,\, j \in J} |S(u;N)|$$ which corresponds to the maximal operator on the Weyl sums associated with the components $u_j$, $j \in J$, of $u$. We are interested in understanding this map for almost all $(u_i)_{i \in I}$ and also in the various norms of these operators. Questions like these have several surprising applications, including outside of number theory, and are also related to restriction theorems for Weyl sums. Salle 15-25-502 Adresse Jussieu