Zobrazeno 1 - 10
of 396
pro vyhledávání: '"11F06"'
Autor:
Nie, Zhaohu, Parent, C. Xavier
We produce canonical sets of right coset representatives for the congruence subgroups $\Gamma_0(N)$, $\Gamma_1(N)$ and $\Gamma(N)$, and prove that the corresponding fundamental domains are connected. We present some pictures and examples at the end.<
Externí odkaz:
http://arxiv.org/abs/2411.17119
We estimate the growth rates for the set of reciprocal conjugacy classes in the Hecke groups. In other words, this estimates the growth of the reciprocal geodesics in terms of word lengths on the hyperbolic orbifolds associated with the Hecke groups.
Externí odkaz:
http://arxiv.org/abs/2411.00739
Autor:
Hao, Yanlong
In this paper, we investigate the trace set of a Fuchsian lattice. There are two results of this paper: the first is that for a non-uniform lattice, we prove Scmutz's conjecture: the trace set of a Fuchsian lattice exhibits linear growth if and only
Externí odkaz:
http://arxiv.org/abs/2410.05223
Autor:
Loué, Alex
A triangle presentation is a combinatorial datum that encodes the action of a group on a $2$-dimensional triangle complex with prescribed links, which is simply transitive on the vertices. We provide the first infinite family of triangle presentation
Externí odkaz:
http://arxiv.org/abs/2408.15763
We prove that a closed negatively curved analytic Riemannian manifold that contains infinitely many totally geodesic hypersurfaces is isometric to an arithmetic hyperbolic manifold. Equivalently, any closed analytic Riemannian manifold with negative
Externí odkaz:
http://arxiv.org/abs/2408.03430
We study the Drinfeld modular curves arising from the Hecke congruence subgroups of $\mathrm{SL}_2(\mathbb{F}_q[T])$. Using a combinatorial method of Gekeler and Nonnengardt, we obtain a genus formula for these curves. In cases when the genus is one,
Externí odkaz:
http://arxiv.org/abs/2408.00198
Autor:
Ross, Erick
Consider $N \geq 1$, $k \geq 2$, and $\chi$ a Dirichlet character modulo $N$ such that $\chi(-1) = (-1)^k$. For any bound $B$, one can show that $\dim S_k(\Gamma_0(N),\chi) \le B$ for only finitely many triples $(N,k,\chi)$. It turns out that this pr
Externí odkaz:
http://arxiv.org/abs/2407.08881
Autor:
Dória, Cayo, Paiva, Nara
The goal of this work is to give new quantitative results about the distribution of semi-arithmetic hyperbolic surfaces in the moduli space of closed hyperbolic surfaces. We show that two coverings of genus $g$ of a fixed arithmetic surface $S$ are $
Externí odkaz:
http://arxiv.org/abs/2402.18676
The modular group $\operatorname{PSL}_2(\mathbb{Z})$ acts on the upper-half plane $\mathbb{HP}$ with quotient the modular orbifold, uniformized by the function $\mathfrak{j} \colon \mathbb{HP}\to \mathbb{C}$. We first show that second derived subgrou
Externí odkaz:
http://arxiv.org/abs/2402.17628
Autor:
Zhu, Xiao-Jie
We give explicit formulae for a class of complex linear unitary characters of the congruence subgroups $\Gamma_0(N)$ which involve a variant of Rademacher's $\Psi$ function. We then prove that these characters cover all characters of $\Gamma_0(N)$ pr
Externí odkaz:
http://arxiv.org/abs/2402.14796