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
Date20/06/2022
Horaire14:00 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.

Salle15-25-502
AdresseJussieu
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