Representation zeta function of a family of maximal class groups: Non-exceptional primes

References

[1] N. Avni, Arithmetic groups have rational representation growth, Ann. of Math. (2) 174 (2011), no. 2, 1009–1056. 10.4007/annals.2011.174.2.6Suche in Google Scholar

[2] N. Avni, B. Klopsch, U. Onn and C. Voll, On representation zeta functions of groups and a conjecture of Larsen–Lubotzky, C. R. Math. Acad. Sci. Paris 348 (2010), no. 7–8, 363–367. 10.1016/j.crma.2010.02.019Suche in Google Scholar

[3] N. Avni, B. Klopsch, U. Onn and C. Voll, Arithmetic groups, base change, and representation growth, Geom. Funct. Anal. 26 (2016), no. 1, 67–135. 10.1007/s00039-016-0359-6Suche in Google Scholar

[4] L. Bartholdi and P. de la Harpe, Representation zeta functions of wreath products with finite groups, Groups Geom. Dyn. 4 (2010), no. 2, 209–249. 10.4171/ggd/81Suche in Google Scholar

[5] M. N. Berman, I. Glazer and M. M. Schein, Pro-isomorphic zeta functions of nilpotent groups and Lie rings under base extension, Trans. Amer. Math. Soc. 375 (2022), no. 2, 1051–1100. 10.1090/tran/8506Suche in Google Scholar

[6] D. A. Craven, Lower bounds for representation growth, J. Group Theory 13 (2010), no. 6, 873–890. 10.1515/jgt.2010.029Suche in Google Scholar

[7] M. du Sautoy and L. Woodward, Zeta Functions of Groups and Rings, Lecture Notes in Math. 1925, Springer, Berlin, 2008. 10.1007/978-3-540-74776-5Suche in Google Scholar

[8] S. Ezzat, Representation growth of finitely generated torsion-free nilpotent groups: Methods and examples, Ph.D. Thesis, University of Canterbury, 2012. Suche in Google Scholar

[9] S. Ezzat, Counting irreducible representations of the Heisenberg group over the integers of a quadratic number field, J. Algebra 397 (2014), 609–624. 10.1016/j.jalgebra.2013.08.028Suche in Google Scholar

[10] S. Ezzat, Representation growth of maximal class groups: Various exceptional cases, preprint (2014), https://arxiv.org/abs/1410.4992. Suche in Google Scholar

[11] E. Hrushovski, B. Martin and S. Rideau, Definable equivalence relations and zeta functions of groups, J. Eur. Math. Soc. (JEMS) 20 (2018), no. 10, 2467–2537. 10.4171/jems/817Suche in Google Scholar

[12] A. Jaikin-Zapirain, Zeta function of representations of compact 𝑝-adic analytic groups, J. Amer. Math. Soc. 19 (2006), no. 1, 91–118. 10.1090/S0894-0347-05-00501-1Suche in Google Scholar

[13] B. Klopsch, Representation growth and representation zeta functions of groups, Note Mat. 33 (2013), no. 1, 107–120. Suche in Google Scholar

[14] A. Lubotzky and A. R. Magid, Varieties of representations of finitely generated groups, Mem. Amer. Math. Soc. 336 (1985), no. 58, 1–117. 10.1090/memo/0336Suche in Google Scholar

[15] A. Lubotzky and B. Martin, Polynomial representation growth and the congruence subgroup problem, Israel J. Math. 144 (2004), 293–316. 10.1007/BF02916715Suche in Google Scholar

[16] C. Nunley and A. Magid, Simple representations of the integral Heisenberg group, Classical Groups and Related Topics (Beijing 1987), Contemp. Math. 82, American Mathematical Society, Providence (1989), 89–96. 10.1090/conm/082/982280Suche in Google Scholar

[17] T. Rossmann, Computing topological zeta functions of groups, algebras, and modules, I, Proc. Lond. Math. Soc. (3) 110 (2015), no. 5, 1099–1134. 10.1112/plms/pdv012Suche in Google Scholar

[18] T. Rossmann, Computing local zeta functions of groups, algebras, and modules, Trans. Amer. Math. Soc. 370 (2018), no. 7, 4841–4879. 10.1090/tran/7361Suche in Google Scholar

[19] R. Snocken, Zeta functions of groups and rings, Ph.D. Thesis, University of Southampton, 2014. Suche in Google Scholar

[20] A. Stasinski and C. Voll, Representation zeta functions of nilpotent groups and generating functions for Weyl groups of type 𝐵, Amer. J. Math. 136 (2014), no. 2, 501–550. 10.1353/ajm.2014.0010Suche in Google Scholar

[21] C. Voll, Functional equations for zeta functions of groups and rings, Ann. of Math. (2) 172 (2010), no. 2, 1181–1218. 10.4007/annals.2010.172.1181Suche in Google Scholar

[22] E. Witten, On quantum gauge theories in two dimensions, Comm. Math. Phys. 141 (1991), no. 1, 153–209. 10.1007/BF02100009Suche in Google Scholar

[23] M. Zordan, Univariate and bivariate zeta functions of unipotent group schemes of type 𝐺, Internat. J. Algebra Comput. 32 (2022), no. 4, 653–682. 10.1142/S0218196722500291Suche in Google Scholar