Arithmetic combinatorics on Vinogradov systems

Abstract: In this talk, we consider the Vinogradov system of equations from an arithmetic combinatorial point of view. The number of solutions of this system, when the variables are restricted to a set of real numbers $A$, has been widely studied by researchers in both analytic number theory and harmonic analysis. In particular, there has been a significant amount of work regarding upper bounds for the number of solutions to the above system of equations. The objective of our talk will be of a different flavour, wherein we will try to address the following question: Given a set $A$ with many solutions to the Vinogradov system, what other arithmetic properties can we infer about $A$?

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.