Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On Iwasawa $\lambda$-invariants for abelian number fields and random matrix heuristics
HTML articles powered by AMS MathViewer

by Daniel Delbourgo and Heiko Knospe HTML | PDF
Math. Comp. 92 (2023), 1817-1836 Request permission


Following both Ernvall-Metsänkylä and Ellenberg-Jain-Venkatesh, we study the density of the number of zeroes (i.e. the cyclotomic $\lambda$-invariant) for the $p$-adic zeta-function twisted by a Dirichlet character $\chi$ of any order. We are interested in two cases: (i) the character $\chi$ is fixed and the prime $p$ varies, and (ii) $ord(\chi )$ and the prime $p$ are both fixed but $\chi$ is allowed to vary. We predict distributions for these $\lambda$-invariants using $p$-adic random matrix theory and provide numerical evidence for these predictions. We also study the proportion of $\chi$-regular primes, which depends on how $p$ splits inside $\mathbb {Q}(\chi )$. Finally, we tabulate the values of the $\lambda$-invariant for every character $\chi$ of conductor $\leqslant 1000$ and for odd primes $p$ of small size.
Similar Articles
Additional Information
  • Daniel Delbourgo
  • Affiliation: Department of Mathematics and Statistics, University of Waikato, Gate 8, Hillcrest Road, Hamilton 3240, New Zealand
  • MR Author ID: 355277
  • ORCID: 0000-0002-9750-7734
  • Email:
  • Heiko Knospe
  • Affiliation: Technische Hochschule Köln, Fakultät für Informations-, Medien- und Elektrotechnik, Institut für Nachrichtentechnik, Betzdorfer Str. 2, 50679 Köln, Germany
  • MR Author ID: 363483
  • ORCID: 0000-0002-6823-6250
  • Email:
  • Received by editor(s): July 13, 2022
  • Received by editor(s) in revised form: November 30, 2022, and December 29, 2022
  • Published electronically: February 28, 2023
  • © Copyright 2023 American Mathematical Society
  • Journal: Math. Comp. 92 (2023), 1817-1836
  • MSC (2020): Primary 11R23; Secondary 11R42, 11S80, 11M41
  • DOI:
  • MathSciNet review: 4570343