Uniform analytic properties of representation zeta functions of finitely generated nilpotent groups

Dung Hoang Duong, Christopher Voll

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Let G be a finitely generated nilpotent group. The representation zeta function ζG(s) of G enumerates twist isoclasses of finite-dimensional irreducible complex representations of G. We prove that ζG(s) has rational abscissa of convergence α(G) and may be meromorphically continued to the left of α(G) and that, on the line {s ∈ ℂ

Original languageEnglish
Pages (from-to)6327-6349
Number of pages23
JournalTransactions of the American Mathematical Society
Volume369
Issue number9
DOIs
Publication statusPublished - Jan 1 2017

Fingerprint

G-convergence
Abscissa
Finitely Generated Group
Nilpotent Group
Twist
Riemann zeta function
Line

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

Uniform analytic properties of representation zeta functions of finitely generated nilpotent groups. / Duong, Dung Hoang; Voll, Christopher.

In: Transactions of the American Mathematical Society, Vol. 369, No. 9, 01.01.2017, p. 6327-6349.

Research output: Contribution to journalArticle

@article{44043c3be70844a981563017b08541ac,
title = "Uniform analytic properties of representation zeta functions of finitely generated nilpotent groups",
abstract = "Let G be a finitely generated nilpotent group. The representation zeta function ζG(s) of G enumerates twist isoclasses of finite-dimensional irreducible complex representations of G. We prove that ζG(s) has rational abscissa of convergence α(G) and may be meromorphically continued to the left of α(G) and that, on the line {s ∈ ℂ",
author = "Duong, {Dung Hoang} and Christopher Voll",
year = "2017",
month = "1",
day = "1",
doi = "10.1090/tran/6879",
language = "English",
volume = "369",
pages = "6327--6349",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "9",

}

TY - JOUR

T1 - Uniform analytic properties of representation zeta functions of finitely generated nilpotent groups

AU - Duong, Dung Hoang

AU - Voll, Christopher

PY - 2017/1/1

Y1 - 2017/1/1

N2 - Let G be a finitely generated nilpotent group. The representation zeta function ζG(s) of G enumerates twist isoclasses of finite-dimensional irreducible complex representations of G. We prove that ζG(s) has rational abscissa of convergence α(G) and may be meromorphically continued to the left of α(G) and that, on the line {s ∈ ℂ

AB - Let G be a finitely generated nilpotent group. The representation zeta function ζG(s) of G enumerates twist isoclasses of finite-dimensional irreducible complex representations of G. We prove that ζG(s) has rational abscissa of convergence α(G) and may be meromorphically continued to the left of α(G) and that, on the line {s ∈ ℂ

UR - http://www.scopus.com/inward/record.url?scp=85020446194&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85020446194&partnerID=8YFLogxK

U2 - 10.1090/tran/6879

DO - 10.1090/tran/6879

M3 - Article

AN - SCOPUS:85020446194

VL - 369

SP - 6327

EP - 6349

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 9

ER -