Zeta function of representations of compact p-adic analytic groups

By A. Jaikin‐Zapirain. 2005

86 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1c5dcc4b6e32327dac29b9398e47cc0499d03dd7

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Citations in the corpus

On irreducible representations of compact $p$-adic analytic groups (2011, unknown): “See [47] and [20] for more details.”
Representation Growth of Linear Groups (2006, background): “ity. Theorem 7.1. If G(K) = SL1(D) where Dis a division algebra of degree dover a local ﬁeld K of characteristic 0, then G(K) is compact virtually pro-pgroup and ρ(G(K)) = r κ = 2 d . Jaikin-Zapirain [Ja2] computed the v-adic local zeta function of SL2(Ov). From his result one sees that ρ= 1 = r κ f”
Representation zeta functions of compact p-adic analytic groups and arithmetic groups (2010, methodology): “A general class of such p-adic zeta functions was introduced in [51]; it does not rely on notions from model theory such as the concept of definable integrals utilised in [31], for which explicit formulae are not available.”
Representation growth and rational singularities of the moduli space of local systems (2013, methodology): “Jaikin–Zapirain proved in [28] that there are natural numbers ni and rational functions fi ∈ Q(x), for i = 1, .”
Representation zeta functions of nilpotent groups and generating functions for Weyl groups of type B (2011, methodology): “quotient. The non-archimedean factors in the context of semisimple groups have been studied using the Kirillov orbit method and techniques from model theory and p-adic integration; see, for instance, [21, 1, 3]. Thefollowing summarisesthemain results ofthe paperand some ofits motivation. On the one ”
Functional equations for zeta functions of groups and rings (2006, methodology): “Jaikin-Zapirain proved in [19] the rationality of representation zeta functions for certain compact p-adic analytic groups using a Kirillov-type correspondence developed by Howe ([15]) for these groups.”