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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 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Borel’s rank theorem for Artin $L$-functions
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by Ningchuan Zhang
Proc. Amer. Math. Soc. 151 (2023), 4621-4632
DOI: https://doi.org/10.1090/proc/16493
Published electronically: June 30, 2023

Abstract:

Borel’s rank theorem identifies the ranks of algebraic $K$-groups of the ring of integers of a number field with the orders of vanishing of the Dedekind zeta function attached to the field. Following the work of Gross, we establish a version of this theorem for Artin $L$-functions by considering equivariant algebraic $K$-groups of number fields with coefficients in rational Galois representations. This construction involves twisting algebraic $K$-theory spectra with rational equivariant Moore spectra. We further discuss integral equivariant Moore spectra attached to Galois representations and their potential applications in $L$-functions.
References
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Bibliographic Information
  • Ningchuan Zhang
  • Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104
  • MR Author ID: 1495949
  • ORCID: 0000-0002-7003-6354
  • Email: nczhang@sas.upenn.edu
  • Received by editor(s): September 26, 2022
  • Received by editor(s) in revised form: March 13, 2023, and March 22, 2023
  • Published electronically: June 30, 2023
  • Communicated by: Julie Bergner
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 4621-4632
  • MSC (2020): Primary 19F27; Secondary 55P62, 55P91
  • DOI: https://doi.org/10.1090/proc/16493
  • MathSciNet review: 4634868