University of Cambridge > Talks.cam > Number Theory Seminar > An identity on class numbers of cubic rings

  Browse A-Z

Log in

University Account External (via Google)

🔐 Log In

Information on

Subscribing to talksdetails Finding a talkdetails Adding a talkdetails Disseminating talksdetails Help and Documentationdetails

ℹ️ Information

An identity on class numbers of cubic rings

Download to your calendar using vCal

  • UserEvan O'Dorney (Cambridge)
  • ClockTuesday 17 May 2016, 14:15-15:15
  • HouseMR13.

If you have a question about this talk, please contact Jack Thorne .

Let h(D) be the number of cubic rings (over Z) with discriminant D, and let h’(D) be the number of cubic rings with discriminant -27D such that the traces of all elements are multiples of 3, in each case weighting each ring by the reciprocal of its number of automorphisms. While studying the Dirichlet 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 the Scholz reflection principle that was verified by Nakagawa the following year. I will speak on an original proof of this identity that combines class field theory with one of Bhargava’s higher composition laws.

This talk is part of the Number Theory Seminar series.

This talk is included in these lists:

Note that ex-directory lists are not shown.

Other lists

Webinar & FW11, Computer Laboratory, William Gates Building. CMS, Meeting Room 15 ReproSoc

Other talks

Title to be confirmed Morning Break César Milstein Lecture - Title TBC Using A Function-Centric Lens to Re-consider Regularisation, Representation Transfer and Geometric Properties of Neural Networks Title to be confirmed Sheref Mansy, topic TBA
 

© 2006-2025 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity