The cusp amplitudes and quasi-level of a congruence subgroup of SL2 over any Dedekind domain

Linear characters of SL_2 over Dedekind domains

For an important class of arithmetic Dedekind domains O including the ring of integers of not totally complex number fields, we describe explicitly the group of linear characters of SL_2(O). For this, we determine, for arbitrary Dedekind domains O, the group of linear characters of SL_2(O) whose kernel is a congruence subgroup.

Generalized Dedekind sums

Classical Dedekind sums are connected to the modular group through the construction of a (Dedekind) symbol on the cusp set of the modular group. In this paper we study generalizations of Dedekind symbols and sums that can be associated to certain Fuchsian groups uniformizing 1-punctured tori.

关于数字段上 $SL_2$ 合同子群加权尖点计数的衰减

Decay of weighted cusp counts for congruence subgroups of $SL_2$ over number fields

研究数字段上 $SL_2$ 合同子群的加权尖点计数，证明总加权尖点计数与群指数的比值被合同水平范数的负幂所限制，推广了 Cox--Parry 关于有理数域的结果，并支持尖点项在拓扑、算术和表示论公式中为次主导项的猜想。

Quotients of the Bruhat-Tits tree by function field analogs of the Hecke congruence subgroups

Let C be a smooth, projective and geometrically integral curve defined over a finite field F. For each closed point P of C, let R be the ring of functions that are regular outside P, and let K be the completion at P of the function field of C. In order to study groups of the form GL2(R), Serre describes the quotient graph GL2(R)\t, where t is the Bruhat-Tits tree defined from SL2(K). In particular, Serre shows that GL2(R)\t is the union of a finite graph and a finite number of ray shaped subgraphs, which are called cusps. It is not hard to see that finite index subgroups inherit this property.…

同余子群的连通基本域

Connected fundamental domains for congruence subgroups

本文通过研究同余子群的项目线结构，构造了连通的基本域代表集，并引入了多重性函数M与可计算函数W，展示了其在数学中的应用。

Relative centralisers of relative subgroups

Let $R$ be an associative ring with 1, $G=GL(n, R)$ be the general linear group of degree $n\ge 3$ over $R$. In this paper we calculate the relative centralisers of the relative elementary subgroups or the principal congruence subgroups, corresponding to an ideal $A\unlhd R$ modulo the relative elementary subgroups or the principal congruence subgroups, corresponding to another ideal $B\unlhd R$. Modulo congruence subgroups the results are essentially easy exercises in linear algebra. But modulo the elementary subgroups they turned out to be quite tricky, and we could get definitive answers on…