Leírás
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.
Meeting link: https://unideb.webex.com/unideb/j.php?MTID=m9bd4224bf30abe6a119624df7d23e791
Meeting number: 2783 490 1066
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We are looking forward to meeting you, with kind regards,
the organizers (K.Győry, Á.Pintér, L.Hajdu, A.Bérczes, Sz.Tengely, I.Pink, Debrecen Number Theory Research Group , University of Debrecen)