Effective equidistribution of rational points on certain expanding horospheres
Linfoot Number Theory Seminar
3rd October 2018, 11:00 am – 12:00 pm
Howard House, 4th Floor Seminar Room
In a 2016 paper, Manfred Einsiedler, Shahar Mozes, Nimish Shah and Uri Shapira used techniques from homogeneous dynamics to establish the equidistribution of primitive rational points on expanding horospheres in the space of unimodular lattices in at least 3 dimensions. Due to the nature of their proof, relying in particular on Marina Ratner's measure-classification theorem, their result does not come with a quantitative error term. I will discuss a joint work with Bingrong Huang and Min Lee, in which we pursue an analytic number-theoretic approach to give a rate of convergence for a specific horospherical subgroup in any dimension. This extends work of Min Lee and Jens Marklof who dealt with the 3-dimensional case in 2017.