Hilbert cubes meet arithmetic sets
Norbert Hegyvari (Eotvos University and Renyi Institute, Budapest)
Abstract: In 1978, Nathanson obtained several results on sumsets contained in infinite sets of integers. Later the author investigated how big a Hilbert cube avoiding a given {\it infinite} sequence of integers can be.
In the present talk, we show that an additive Hilbert cube, in {\it prime fields} of sufficiently large dimension, always meets certain kinds of arithmetic sets, namely, product sets and reciprocal sets of sumsets satisfying certain technical conditions.
Joint work with Peter P. Pach.
number theory
Audience: researchers in the topic
Combinatorial and additive number theory (CANT 2021)
Series comments: This is the nineteenth in a series of annual workshops sponsored by the New York Number Theory Seminar on problems in combinatorial and additive number theory and related parts of mathematics.
Registration for the conference is free. Register at cant2021.eventbrite.com.
The conference website is www.theoryofnumbers.com/cant/ Lectures will be broadcast on Zoom. The Zoom login will be emailed daily to everyone who has registered on eventbrite. To join the meeting, you may need to download the free software from www.zoom.us.
The conference program, list of speakers, and abstracts are posted on the external website.
| Organizer: | Mel Nathanson* |
| *contact for this listing |