Simple representations of the integral Heisenberg group

Nunley, Charles; Magid, Andy R.

doi:10.1090/conm/082/982280

Cited by 16 publications

(19 citation statements)

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“…The latter happens if and only if I;r corresponds to a lattice of type .I; r/ such that m.OEƒ/ D m. This proves the first equality. The second equality is an immediate consequence of (26). Lemma 3.1 allows us to express the generating functions (30) in terms of the p-adic integrals (32).…”

Section: 4])mentioning

confidence: 99%

Functional equations for zeta functions of groups and rings

Voll

2010

Ann. Math.

119

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We introduce a new method to compute explicit formulae for various zeta functions associated to groups and rings. The specific form of these formulae enables us to deduce local functional equations. More precisely, we prove local functional equations for the subring zeta functions associated to rings, the subgroup, conjugacy and representation zeta functions of finitely generated, torsion-free nilpotent (or --)groups, and the normal zeta functions of --groups of class 2. We deduce our theorems from a "blueprint result" on certain p-adic integrals which generalises work of Denef and others on Igusa's local zeta function. The Malcev correspondence and a Kirillov-type theory developed by Howe are used to "linearise" the problems of counting subgroups and representations in --groups, respectively.

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Section: 4])mentioning

confidence: 99%

Functional equations for zeta functions of groups and rings

Voll

2010

Ann. Math.

119

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“…where ϕ is the Euler totient function; cf. [42]. It turns out that the formula in (4.2) behaves uniformly under some base extensions, as we shall now explain.…”

Section: 1mentioning

confidence: 75%

Zeta functions of groups and rings – recent developments

Voll¹

2015

Groups St Andrews 2013

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“…be the "natural" Z-form of the Heisenberg group. It has long been known [14] that the global twist-representation zeta function of H(Z) satisfies ζ irr…”

Section: Resultsmentioning

confidence: 99%

Stability results for local zeta functions of groups algebras, and modules

Rossmann

2017

Math. Proc. Camb. Phil. Soc.

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Various types of local zeta functions studied in asymptotic group theory admit two natural operations: (1) change the prime and (2) perform local base extensions. Often, the effects of both of these operations can be expressed simultaneously in terms of a single explicit formula. We show that in these cases, the behaviour of local zeta functions under variation of the prime in a set of density 1 in fact completely determines these functions for almost all primes and, moreover, it also determines their behaviour under local base extensions. We discuss applications to topological zeta functions, functional equations, and questions of uniformity.

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Simple representations of the integral Heisenberg group

Cited by 16 publications

References 0 publications

Functional equations for zeta functions of groups and rings

Functional equations for zeta functions of groups and rings

Zeta functions of groups and rings – recent developments

Stability results for local zeta functions of groups algebras, and modules

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