We study the Iwasawa $\lambda$-invariants of Dirichlet characters $\chi$ of any order and generalize a prediction of Ellenberg, Jain and Venkatesh using random matrix heuristics. We vary $\chi$ where both the order of $\chi$ and the prime $p$ are fixed, and vary $p$ for a fixed character $\chi$. Furthermore, we study the proportion of $\chi$-regular and $F$-regular primes, where $F$ is a totally real abelian number field. We provide numerical evidence for our predictions and tabulate the values of the $\lambda$-invariant for every character of conductor $< 1000$ and odd primes of small size. The paper is published in the AMS journal Mathematics of Computation. The preprint is available here.

# Paper on Iwasawa lambda-invariants for abelian number fields

Joint paper with Daniel Delbourgo