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URL:/pure-mathematics/events/number-theory-seminar-146
SUMMARY:Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:Summary \n\nMICAH MILINOVICH\, UNIVERSITY OF MISSISSIPPI\n\nHil
 bert spaces and low-lying zeros of L-functions\n\nGiven a family of L-func
 tions\, there has been a great deal of interest\nin estimating the proport
 ion of the family that does not vanish at\nspecial points on the critical 
 line. Conjecturally\, there is a\nsymmetry type associated to each family 
 which governs the distribution\nof low-lying zeros (zeros near the real ax
 is). Generalizing a problem\nof Iwaniec\, Luo\, and Sarnak (2000)\, we add
 ress the problem of\nestimating the proportion of non-vanishing in a famil
 y of L-functions\nat a low-lying height on the critical line (measured by 
 the analytic\nconductor). We solve the Fourier optimization problems that 
 arise\nusing the theory of reproducing kernel Hilbert spaces of entire\nfu
 nctions (there is one such space associated to each symmetry type)\,\nand 
 we can explicitly construct the associated reproducing kernels. If\ntime a
 llows\, we will also address the problem of estimating the height\nof the 
 \"lowest\" low-lying zero in a family for all symmetry types.\nThese resul
 ts are based on joint work with Emanuel Carneiro and\nAndrés Chirre.\n\nM
 C 5417\n 
DTSTAMP:20250708T155927Z
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