Primitive rational points on expanding horospheres: effective joint equidistribution

Abstract: I will report on ongoing work with Min Lee and Andreas Strömbergsson. Using techniques from analytic number theory, spectral theory, geometry of numbers as well as a healthy dose of linear algebra and building on a previous work by Bingrong Huang, Min Lee and myself, we furnish a new proof of a 2016 theorem by Einsiedler, Mozes, Shah and Shapira. That theorem concerns the equidistribution of primitive rational points on certain manifolds and our proof has the added benefit of yielding a rate of convergence. It turns out to have (perhaps surprising) applications to the theory of random graphs, which I shall also discuss.

number theory

Audience: researchers in the topic

Number theory by the sea

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