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SUMMARY:An identity on class numbers of cubic rings - Evan O'Dorney (Cambr
 idge)
DTSTART:20160517T131500Z
DTEND:20160517T141500Z
UID:TALK65990@talks.cam.ac.uk
CONTACT:Jack Thorne
DESCRIPTION:Let h(D) be the number of cubic rings (over Z) with discrimina
 nt D\, and let h'(D) be the number of cubic rings with discriminant -27D s
 uch that the traces of all elements are multiples of 3\, in each case weig
 hting each ring by the reciprocal of its number of automorphisms. While st
 udying the Dirichlet series associated to these two functions\, Y. Ohno di
 scovered in 1997 the pattern that h'(D) = h(D) (if D is negative) or h'(D)
  = 3h(D) (if D is positive): a highly unexpected generalization of the Sch
 olz reflection principle that was verified by Nakagawa the following year.
  I will speak on an original proof of this identity that combines class fi
 eld theory with one of Bhargava's higher composition laws.
LOCATION:MR13
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