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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On abelian cubic fields with large class number
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by Jérémy Dousselin;
Proc. Amer. Math. Soc. 152 (2024), 3255-3264
DOI: https://doi.org/10.1090/proc/16827
Published electronically: June 12, 2024

Abstract:

We investigate the large values of class numbers of cubic fields, showing that one can find arbitrary long sequences of “close” abelian cubic number fields with class numbers as large as possible. We also give a first step toward an explicit lower bound for such extreme values of class numbers of abelian cubic fields.
References
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Bibliographic Information
  • Jérémy Dousselin
  • Affiliation: Université de Lorraine, CNRS, IECL, F-54000 Nancy, France
  • ORCID: 0000-0002-7850-3818
  • Email: jeremy.dousselin@univ-lorraine.fr
  • Received by editor(s): March 16, 2023
  • Received by editor(s) in revised form: January 8, 2024, and February 8, 2024
  • Published electronically: June 12, 2024
  • Communicated by: Amanda Folsom
  • © Copyright 2024 by the author
  • Journal: Proc. Amer. Math. Soc. 152 (2024), 3255-3264
  • MSC (2020): Primary 11R29; Secondary 11R42
  • DOI: https://doi.org/10.1090/proc/16827
  • MathSciNet review: 4767260