Event Date:
Friday, November 2, 2012 - 2:00pm to 3:00pm
Event Location:
- 6635 South Hall
Let q > 3 be a prime congruent to 3 modulo 4. Suppose also that the real quadratic number field generated by the square root of q has class number 1. Then the continued fraction expansion of the square root of q allows one to read off the class number of the imaginary quadratic number field generated by the square root of -q. This was noticed by Friedrich Hirzebruch as a restatement of a Kronecker limit formula on narrow ideal classes by Curt Meyer. Similarly, for an odd prime p, we can use the same continued fraction expansion to read off the corresponding p-adic lambda invariant of the imaginary quadratic number field. This is a consequence of a very general Kronecker limit formula on narrow ray classes by Shuji Yamamoto.
October 9, 2014 - 4:09pm