Paper on Iwasawa lambda-invariants for abelian number fields

Joint paper with Daniel Delbourgo

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.

Heiko Knospe
Professor fĂĽr Mathematik in der Nachrichtentechnik

My research interests include number theory, cryptography and network security.