Related papers: Computing fundamental domains for Fuchsian groups

In this paper we study invariant rings arising in the study of finite dimensional algebraic structures. The rings we encounter are graded rings of the form $K[U]^{\Gamma}$ where $\Gamma$ is a product of general linear groups over a field…

We prove a generalization of the Hasumi's Direct Cauchy Theorem property for the derivatives (Theorem 2.2).

This work provides calculus for the Fr\'echet and limiting subdifferential of the pointwise supremum given by an arbitrary family of lower semicontinuous functions. We start our study showing fuzzy results about the Fr\'echet…

We prove a general Mosco convergence theorem for bounded Euclidean domains satisfying a set of mild geometric hypotheses. For bounded domains, this notion implies norm-resolvent convergence for the Dirichlet Laplacian which in turn ensures…

We consider invariants of a finite group related to the number of random (independent, uniformly distributed) conjugacy classes which are required to generate it. These invariants are intuitively related to problems of Galois theory. We…

Given discrete groups $\Gamma \subset \Delta$ we characterize $(\Gamma,\sigma)$-invariant spaces that are also invariant under $\Delta$. This will be done in terms of subspaces that we define using an appropriate Zak transform and a…

We give a general procedure to analyze the structure for certain $\mathbb{C}$-Fuchsian subgroups of some non-arithmetic lattices. We will also show that their fundamental domains lie in a complex geodesic, a set homeomorphic to the unit…

Motivated by developing algorithms that decide hypertranscendence of solutions of extensions of the Bessel differential equation, algorithms computing the unipotent radical of a parameterized differential Galois group have been recently…

We give practical algorithms for computing the divisor class group and the gonality of a curve over a finite field, achieving several orders of magnitude speedup over existing methods for sufficiently large genus or residue field. The…

We show by means of various examples that many of the current definitions of the notion of fundamental domain of a Fuchsian group lack an extra condition ensuring that the domain differs from a measurable fundamental set at most by a null…

Let C be a non-empty finite set, and Gamma a subgroup of the symmetric group S(C). Given a bijection f:A cross C to B cross C, the problem of Gamma-equivariant division is to find a quotient bijection h:A to B respecting whatever symmetries…

We give simple necessary and sufficient conditions for the $\frac{\partial}{\partial t}$-transcendence of the solutions to a parameterized second order linear differential equation of the form \frac{\partial^2 Y}{\partial x^2} - p…

We consider discrete subgroups Gamma of the simply connected Lie group SU~(1,1), the universal cover of SU(1,1), of finite level, i.e. the subgroup intersects the centre of SU~(1,1) in a subgroup of finite index, this index is called the…

In this short article, we study the extremal behavior $F_\Gamma(n)$ of divisibility functions $D_\Gamma$ introduced by the first author for finitely generated groups $\Gamma$. We show finitely generated subgroups of $\GL(m,K)$ for an…

We find the complete equivalence group of a class of (1+1)-dimensional second-order evolution equations, which is infinite-dimensional. The equivariant moving frame methodology is invoked to construct, in the regular case of the…

We develop a practical algorithm to decide whether a finitely generated subgroup of a solvable algebraic group $G$ is arithmetic. This incorporates a procedure to compute a generating set of an arithmetic subgroup of $G$. We also provide a…

Let $\Gamma$ denote the $d = 2$ Bianchi group $\operatorname{PSL}(2,\mathbb{Z}[\sqrt{-2}])$. We give an explicit description of all conjugacy classes of maximal nonelementary Fuchsian subgroups of $\Gamma$ as integral orders of certain…

We present a general diagrammatic approach to the construction of efficient algorithms for computing the Fourier transform of a function on a finite group. By extending work which connects Bratteli diagrams to the construction of Fast…

We consider the functional inverse of the Gamma function in the complex plane, where it is multi-valued, and define a set of suitable branches by proposing a natural extension from the real case.

We exhibit a numerical method to compute three-point branched covers of the complex projective line. We develop algorithms for working explicitly with Fuchsian triangle groups and their finite index subgroups, and we use these algorithms to…