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- W2040940467 abstract "Let G by compact p-adic Lie group and suppose that G is FAb, i.e., that H/[H,H] is finite for every open subgroup H of G. The representation zeta function Z(G,s) encodes the distribution of continuous irreducible complex characters of G. Here s denotes a complex variable and Z(G,s) is defined as the Dirichlet generating function whose nth coefficient is equal to the number of irreducible characters of G of degree n. For p greater than 2 it is known that Z(G,s) defines a meromorphic function on the complex plane. Wedderburn's structure theorem for semisimple algebras implies that ZG,-2) = |G| for finite G. We complement this classic result by proving that Z(G,-2) = 0 for infinite G, assuming that p is greater than 2." @default.
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- W2040940467 date "2013-12-19" @default.
- W2040940467 modified "2023-10-07" @default.
- W2040940467 title "The representation zeta function of a FAb compact p -adic Lie group vanishes at −2" @default.
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- W2040940467 doi "https://doi.org/10.1112/blms/bdt090" @default.
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