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Heilbronn characters


Authors: Richard Foote, Hy Ginsberg and V. Kumar Murty
Journal: Bull. Amer. Math. Soc. 52 (2015), 465-496
MSC (2010): Primary 20C15, 11R42
DOI: https://doi.org/10.1090/bull/1492
Published electronically: April 6, 2015
MathSciNet review: 3348444
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Abstract: In a seminal paper in 1972 Hans Heilbronn introduced a virtual character associated to representations of Galois extensions of number fields and Artin's Conjecture on the holomorphy of $ L$-series. His construction has evolved in both application and scope, and may now be applied to produce what are called Heilbronn characters of arbitrary finite groups. This article surveys the inception and development of this concept, weaving together its number-theoretic and group-theoretic dimensions, and culminates in a description of the recent classification of unfaithful minimal Heilbronn characters. Connections with other areas of mathematics, variations on these themes, and possible future directions are also explored.


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Additional Information

Richard Foote
Affiliation: Department of Mathematics and Statistics, University of Vermont, 16 Colchester Avenue, Burlington, Vermont 05405
Email: foote@math.uvm.edu

Hy Ginsberg
Affiliation: Department of Mathematics, Worcester State University, 486 Chandler Street, Worcester Massachusetts 01602
Email: hginsberg@worcester.edu

V. Kumar Murty
Affiliation: Department of Mathematics, University of Toronto, 40 St. George Street, Room 6290, Toronto, Ontario M5S 2E4, Canada
Email: murty@math.utoronto.ca

DOI: https://doi.org/10.1090/bull/1492
Received by editor(s): June 18, 2014
Received by editor(s) in revised form: March 17, 2015
Published electronically: April 6, 2015
Dedicated: Dedicated to Professor Hans A. Heilbronn
Article copyright: © Copyright 2015 American Mathematical Society