Number Theory Seminar: Jordan Schettler (UCSB), 'Using Continued Fractions to Compute Iwasawa Lambda Invariants for Imaginary Quadratic Fields'

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.