Representation zeta functions of some compact p-adic analytic groups

Avni N, Klopsch B, Onn U, Voll C (2012)
In: Zeta Functions in Algebra and Geometry. Campillo A, Cardona G, Melle-Hernández A, Veys W, Zúñiga-Galindo WA (Eds); Contemporary Mathematics, 566. Providence: American Mathematical Society.

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Autor*in
Avni, Nir; Klopsch, Benjamin; Onn, Uri; Voll, ChristopherUniBi
Herausgeber*in
Campillo, Antonio; Cardona, Gabriel; Melle-Hernández, Alejandro; Veys, Wim; Zúñiga-Galindo, Wilson A.
Abstract / Bemerkung
Using the Kirillov orbit method, novel methods from p-adic integration and Clifford theory, we study representation zeta functions associated to compact p-adic analytic groups. In particular, we give general estimates for the abscissae of convergence of such zeta functions. We compute explicit formulae for the representation zeta functions of some compact p-adic analytic groups, defined over a compact discrete valuation ring O of characteristic 0. These include principal congruence subgroups of SL_2(O), without any restrictions on the residue field characteristic of O, as well as the norm one group SL_1(D) of a non-split quaternion algebra D over the field of fractions of O and its principal congruence subgroups. We also determine the representation zeta functions of principal congruence subgroups of SL_3(O) in the case that O has residue field characteristic 3 and is unramified over Z_3.
Erscheinungsjahr
2012
Buchtitel
Zeta Functions in Algebra and Geometry
Serientitel
Contemporary Mathematics
Band
566
ISBN
978-0-8218-6900-0
Page URI
https://pub.uni-bielefeld.de/record/2963568

Zitieren

Avni N, Klopsch B, Onn U, Voll C. Representation zeta functions of some compact p-adic analytic groups. In: Campillo A, Cardona G, Melle-Hernández A, Veys W, Zúñiga-Galindo WA, eds. Zeta Functions in Algebra and Geometry. Contemporary Mathematics. Vol 566. Providence: American Mathematical Society; 2012.
Avni, N., Klopsch, B., Onn, U., & Voll, C. (2012). Representation zeta functions of some compact p-adic analytic groups. In A. Campillo, G. Cardona, A. Melle-Hernández, W. Veys, & W. A. Zúñiga-Galindo (Eds.), Contemporary Mathematics: Vol. 566. Zeta Functions in Algebra and Geometry Providence: American Mathematical Society. https://doi.org/10.1090/conm/566
Avni, N., Klopsch, B., Onn, U., and Voll, C. (2012). “Representation zeta functions of some compact p-adic analytic groups” in Zeta Functions in Algebra and Geometry, Campillo, A., Cardona, G., Melle-Hernández, A., Veys, W., and Zúñiga-Galindo, W. A. eds. Contemporary Mathematics, vol. 566, (Providence: American Mathematical Society).
Avni, N., et al., 2012. Representation zeta functions of some compact p-adic analytic groups. In A. Campillo, et al., eds. Zeta Functions in Algebra and Geometry. Contemporary Mathematics. no.566 Providence: American Mathematical Society.
N. Avni, et al., “Representation zeta functions of some compact p-adic analytic groups”, Zeta Functions in Algebra and Geometry, A. Campillo, et al., eds., Contemporary Mathematics, vol. 566, Providence: American Mathematical Society, 2012.
Avni, N., Klopsch, B., Onn, U., Voll, C.: Representation zeta functions of some compact p-adic analytic groups. In: Campillo, A., Cardona, G., Melle-Hernández, A., Veys, W., and Zúñiga-Galindo, W.A. (eds.) Zeta Functions in Algebra and Geometry. Contemporary Mathematics. 566, American Mathematical Society, Providence (2012).
Avni, Nir, Klopsch, Benjamin, Onn, Uri, and Voll, Christopher. “Representation zeta functions of some compact p-adic analytic groups”. Zeta Functions in Algebra and Geometry. Ed. Antonio Campillo, Gabriel Cardona, Alejandro Melle-Hernández, Wim Veys, and Wilson A. Zúñiga-Galindo. Providence: American Mathematical Society, 2012.Vol. 566. Contemporary Mathematics.

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