Growth in Hecke groups

被引：1

作者：

Kreuzer, Martin ^{[1
]}

Rosenberger, Gerhard ^{[1
]}

机构：

[1] Univ Passau, Fak Informat & Mathemat, D-94030 Passau, Germany

来源：

RIEMANN AND KLEIN SURFACES, AUTOMORPHISMS, SYMMETRIES AND MODULI SPACES | 2014年 / 629卷

关键词：

Hecke group; Hilbert function; Dehn function; subgroup growth; zeta function; NORMAL-SUBGROUPS; NUMBER; INDEX; CLASSIFICATION;

D O I：

10.1090/conm/629/12556

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For the Hecke groups H(lambda(q)) -= < s, t : s(2) = (st)(q) = 1 >, we determine and collect a number of growth functions, their generating series and growth rates: numbers of elements of a given length, numbers of subgroups of a certain index, numbers of normal subgroups, numbers of normal subgroups of genus one, and numbers of free subgroups. Depending on the type of these growth functions, we calculate the corresponding generating series or the generating Dirichlet series. A particular emphasis is put on explicit formulas representing these series as rational functions or via Euler product decompositions.

引用

页码：261 / 281

页数：21

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