Heilbronn characters

Foote, Richard; Ginsberg, Hy; Murty, V.

doi:10.1090/bull/1492

Heilbronn characters
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by Richard Foote, Hy Ginsberg and V. Kumar Murty PDF

Bull. Amer. Math. Soc. 52 (2015), 465-496 Request permission

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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