Saúl Rodriguez Martin
The Ohio State University
Title
An ergodic approach to equations of the form x+y=⌊α(n)⌋
Abstract
Khalfalah and Szemerédi proved in 2006 that every finite coloring of the positive integers contains distinct monochromatic integers x and y such that x+y=n^2, for some natural n. In this talk, we will discuss an ergodic approach to equations of the form x+y=⌊α(n)⌋, where α(x) is a Hardy field function of polynomial growth, such as x⁷log(x), x^3+log(x)² or x^π. We will see when such equations have solutions with x,y lying either in the same cell of a given finite partition of the positive integers or in a given set of positive upper density.
