Distributions of Iwasawa lambda-invariants for Dirichlet Characters


In joint work 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. 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.

Berlin, Germany
Heiko Knospe
Professor fĂĽr Mathematik in der Nachrichtentechnik

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