Table of Contents
Journal of Numbers
Volume 2014, Article ID 803649, 10 pages
http://dx.doi.org/10.1155/2014/803649
Research Article

Using Continued Fractions to Compute Iwasawa Lambda Invariants of Imaginary Quadratic Number Fields

Department of Mathematics, University of California, South Hall, Room 6607, Santa Barbara, CA 93106-3080, USA

Received 18 August 2014; Accepted 27 October 2014; Published 17 November 2014

Academic Editor: Cheon S. Ryoo

Copyright © 2014 Jordan Schettler. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be a prime such that and has class number 1. Then Hirzebruch and Zagier noticed that the class number of can be expressed as where the are partial quotients in the “minus” continued fraction expansion . For an odd prime , we prove an analogous formula using these which computes the sum of Iwasawa lambda invariants of and . In the case that is inert in , the formula pleasantly simplifies under some additional technical assumptions.