Generalized Igusa functions and ideal growth in nilpotent Lie rings

Carnevale A, Schein MM, Voll C (2019)
arXiv:1903.03090.

Preprint | Englisch
 
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Autor*in
Carnevale, Angela; Schein, Michael M.; Voll, ChristopherUniBi
Abstract / Bemerkung
We introduce a new class of combinatorially defined rational functions and apply them to deduce explicit formulae for local ideal zeta functions associated to the members of a large class of nilpotent Lie rings which contains the free class-2-nilpotent Lie rings and is stable under direct products. Our results unify and generalize a substantial number of previous computations. We show that the new rational functions, and thus also the local zeta functions under consideration, enjoy a self-reciprocity property, expressed in terms of a functional equation upon inversion of variables. We establish a conjecture of Grunewald, Segal, and Smith on the uniformity of normal zeta functions of finitely generated free class-2-nilpotent groups.
Erscheinungsjahr
2019
Zeitschriftentitel
arXiv:1903.03090
Page URI
https://pub.uni-bielefeld.de/record/2950123

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Carnevale A, Schein MM, Voll C. Generalized Igusa functions and ideal growth in nilpotent Lie rings. arXiv:1903.03090. 2019.
Carnevale, A., Schein, M. M., & Voll, C. (2019). Generalized Igusa functions and ideal growth in nilpotent Lie rings. arXiv:1903.03090
Carnevale, A., Schein, M. M., and Voll, C. (2019). Generalized Igusa functions and ideal growth in nilpotent Lie rings. arXiv:1903.03090.
Carnevale, A., Schein, M.M., & Voll, C., 2019. Generalized Igusa functions and ideal growth in nilpotent Lie rings. arXiv:1903.03090.
A. Carnevale, M.M. Schein, and C. Voll, “Generalized Igusa functions and ideal growth in nilpotent Lie rings”, arXiv:1903.03090, 2019.
Carnevale, A., Schein, M.M., Voll, C.: Generalized Igusa functions and ideal growth in nilpotent Lie rings. arXiv:1903.03090. (2019).
Carnevale, Angela, Schein, Michael M., and Voll, Christopher. “Generalized Igusa functions and ideal growth in nilpotent Lie rings”. arXiv:1903.03090 (2019).

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