On Gauss factorials and their application to Iwasawa theory for imaginary quadratic fields

Abstract

In this paper we characterize the primes that give non-trivial Iwasawa lambda-invariant for the imaginary quadratic fields $\mathbb{Q}(i)$ and $\mathbb{Q}(\sqrt{-3})$ in terms of Euler numbers and Glaisher numbers. A key step is proving a surprising connection between the non-trivial primes and the 1-exceptional primes for m=3 and m=4