NUMBER THEORY SEMINAR - Monday 3 June, at 13:30 - VENUE: Luigi Stasi Seminar Room - Micah Milinovich

[ICTP Math Section]

_NUMBER THEORY SEMINAR_

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Monday 3 June, at 13:30


VENUE: ICTP Luigi Stasi Seminar Room


Speaker: Micah Milinovich (University of Mississippi - USA)


Title: Hilbert spaces and low-lying zeros of L-functions


Abstract: Given a family of L-functions, there has been a great deal of 
interest in estimating the proportion of the family that does not vanish 
at special points on the critical line. Conjecturally, there is a 
symmetry type associated to each family which governs the distribution 
of low-lying zeros (zeros near the real axis). Generalizing a problem of 
Iwaniec, Luo, and Sarnak (2000), we address the problem of estimating 
the proportion of non-vanishing in a family of L-functions at a 
low-lying height on the critical line (measured by the analytic 
conductor). We solve the Fourier optimization problems that arise using 
the theory of reproducing kernel Hilbert spaces of entire functions 
(there is one such space associated to each symmetry type), and we can 
explicitly construct the associated reproducing kernels. If time allows, 
we will also address the problem of estimating the height of the 
"lowest" low-lying zero in a family for all symmetry types. In this 
context, a new Fourier optimization problem emerges, and we solve it by 
establishing a connection to the theory of de Branges spaces of entire 
functions and using the explicit reproducing kernels we constructed. 
This is joint work with Emanuel Carneiro and Andrés Chirre.

All are welcome to attend.

/https://indico.ictp.it/event/10731//

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