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:

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
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