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SUMMARY:Sato-Tate type distributions for families of hypergeometric variet
 ies - Ken Ono (University of Virginia)
DTSTART:20220823T133000Z
DTEND:20220823T143000Z
UID:TALK177218@talks.cam.ac.uk
DESCRIPTION:Studying the statistical behavior of number theoretic quantiti
 es is presently in vogue. Here we discuss point&nbsp\;counts over finite f
 ields for&nbsp\;&ldquo\;hypergeometric families&rdquo\; of elliptic curves
  and K3 surfaces. We obtain Sato-Tate distributions for these families\, w
 hich turn out to be of SU(2) type (a.k.a. semicircular) and of O3 type (a.
 k.a. Batman type). To prove these results\, we obtain moments for the corr
 esponding traces of Frobenius\, which we analyze using the theory of diffe
 rential operators on spaces of harmonic Maass forms.
LOCATION:Seminar Room 1\, Newton Institute
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