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CATEGORIES:Number Theory Seminar
SUMMARY:An identity on class numbers of cubic rings - Evan
O'Dorney (Cambridge)
DTSTART;TZID=Europe/London:20160517T141500
DTEND;TZID=Europe/London:20160517T151500
UID:TALK65990AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/65990
DESCRIPTION:Let h(D) be the number of cubic rings (over Z) wit
h discriminant D\, and let h'(D) be the number of
cubic rings with discriminant -27D such that the t
races of all elements are multiples of 3\, in each
case weighting each ring by the reciprocal of its
number of automorphisms. While studying the Diric
hlet series associated to these two functions\, Y.
Ohno discovered 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 t
he Scholz reflection principle that was verified b
y Nakagawa the following year. I will speak on an
original proof of this identity that combines clas
s field theory with one of Bhargava's higher compo
sition laws.
LOCATION:MR13
CONTACT:Jack Thorne
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