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URL:https://uwaterloo.ca/pure-mathematics/events/number-theory-seminar-146
SUMMARY:Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:MICAH MILINOVICH\, UNIVERSITY OF MISSISSIPPI\n\nHilbert spaces 
 and low-lying zeros of L-functions\n\nGiven a family of L-functions\, ther
 e has been a great deal of interest\nin estimating the proportion of the f
 amily that does not vanish at\nspecial points on the critical line. Conjec
 turally\, there is a\nsymmetry type associated to each family which govern
 s the distribution\nof low-lying zeros (zeros near the real axis). General
 izing a problem\nof Iwaniec\, Luo\, and Sarnak (2000)\, we address the pro
 blem of\nestimating the proportion of non-vanishing in a family of L-funct
 ions\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\nfunctions (the
 re is one such space associated to each symmetry type)\,\nand we can expli
 citly construct the associated reproducing kernels. If\ntime allows\, we w
 ill also address the problem of estimating the height\nof the \"lowest\" l
 ow-lying zero in a family for all symmetry types.\nThese results are based
  on joint work with Emanuel Carneiro and\nAndrés Chirre.\n\nMC 5417
DTSTAMP:20260407T012823Z
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