On arithmetic Heilbronn supercharacters

Mircea Cimpoeaș
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 31, 2025, Number 2, Pages 305–310
DOI: 10.7546/nntdm.2025.31.2.305-310
Full paper (PDF, 197 Kb)

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Authors and affiliations

Mircea Cimpoeaș
National University of Science and Technology Politehnica Bucharest
Splaiul Independenceei no. 313, Bucharest, Romania
Institute of Mathematics of the Romanian Academy
Calea Grivitei Street no. 21, Bucharest, Romania

Abstract

In this note, we introduce arithmetic Heilbronn supercharacters that generalize the notions of arithmetic Heilbronn characters and Heilbronn supercharacters and discuss several properties of them.

Keywords

  • Heilbronn character
  • Supercharacter theory
  • L-function

2020 Mathematics Subject Classification

  • 11R42
  • 20C15

References

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  2. Artin, E. (1931). Zur Theorie der L-Reihen mit allgemeinen Gruppencharakteren.
    Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 8(1), 292–306.
  3. Brauer, R. (1947). On the zeta-functions of algebraic number fields. American Journal of Mathematics, 69(2), 243–250.
  4. Diaconis, P., & Isaacs, I. M. (2008). Supercharacters and superclasses for algebra groups. Transactions of the American Mathematical Society, 360(5), 2359–2392.
  5. Heilbronn, H. (1973). On real zeros of Dedekind ζ-functions. Canadian Journal of Mathematics, 25(4), 870–873.
  6. Murty, M. R., & Raghuram, A. (2000). Some variations on the Dedekind conjecture. Journal of the Ramanujan Mathematical Society, 15(4), 225–245.
  7. Wong, P.-J. (2017). Character Theory and Artin L-functions. Ph.D. Thesis, Queen’s University, Kingston, Ontario, Canada.
  8. Wong, P.-J. (2017). A variant of Heilbronn characters. International Journal of Number Theory, 13(6), 1547–1570.

Manuscript history

  • Received: 23 October 2024
  • Revised: 22 May 2025
  • Accepted: 29 May 2025
  • Online First: 30 May 2025

Copyright information

Ⓒ 2025 by the Author.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Cite this paper

Cimpoeaș, M. (2025). On arithmetic Heilbronn supercharacters. Notes on Number Theory and Discrete Mathematics, 31(2), 305-310, DOI: 10.7546/nntdm.2025.31.2.305-310.

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