## EVENT DETAILS AND ABSTRACT

**Number Theory**
**Title:** An upper bound for intersection of nodal lines with a fixed horocycle

**Speaker:** Junehyuk Jung

**Speaker Info:** Princeton

**Brief Description:**

**Special Note**:

**Abstract:**

Let X be a noncompact hyperbolic surface of finite area and
let C be a fixed horocycle on X. Let N(f) be a zero set of a Laplacian
eigenfunction f with the eigenvalue t^2, which in fact is a finite
union of real analytic curves. It has been shown in several ways that
N(f) shares common properties with the zero set of a polynomial of
degree t. Therefore we expect that the number of intersection of N(f)
and C is asymptotically bounded by t. I will talk how one can get a
such bound by using analytic theory of Eisenstein series and the
asymptotic of K Bessel function.

**Date:** Monday, October 29, 2012

**Time:** 5:00PM

**Where:** Lunt 107

**Contact Person:** Simon Marshall

**Contact email:** slm@math.northwestern.edu

**Contact Phone:** 847-467-0715

Copyright © 1997-2024
Department of Mathematics, Northwestern University.