# Ueber den arithmetischen Charakter der zu den Verzweigungen (2, 3, 7) und (2, 4, 7) gehörenden Dreiecksfunctionen

@article{FrickeUeberDA,
title={Ueber den arithmetischen Charakter der zu den Verzweigungen (2, 3, 7) und (2, 4, 7) geh{\"o}renden Dreiecksfunctionen},
author={Robert Fricke},
journal={Mathematische Annalen},
volume={41},
pages={443-468}
}
• R. Fricke
• Published 1 September 1892
• Mathematics
• Mathematische Annalen
8 Citations
The Equation of Life
This study will first define the “equation of life" via the principle of least action. Then the paper will show how this “equation of life" can be used to derive smaller equations, involving
On the primitive divisors of the recurrent sequence $$u_{n+1}=(4\rm{cos}^2(2\pi/7)-1)\it{u}_{n}-u_{n-\rm{1}}$$un+1=(4cos2(2π/7)−1)un−un−1 with applications to group theory
Consider the sequence of algebraic integers un given by the starting values u0 = 0, u1 = 1 and the recurrence $$u_{n+1}=(4\rm{cos}^2(2\pi/7)-1)\it{u}_{n}-u_{n-\rm{1}}$$un+1=(4cos2(2π/7)−1)un−un−1. We
Shimura Curves for Level-3 Subgroups of the (2,3,7) Triangle Group and Some Other Examples
• Mathematics
• 2008
The (2, 3, 7) triangle group is known to be associated with a quaternion algebra A/K ramified at two of the three real places of K = Q(cos 2π/7) and unramified at all other places of K. This triangle
Letters from William Burnside to Robert Fricke: automorphic functions, and the emergence of the Burnside Problem
• History
• 2007
Two letters from William Burnside have recently been found in the Nachlass of Robert Fricke that contain instances of the Burnside Problem prior to its first publication. We present these letters as
Shimura Curves for Level-3 Subgroups of the (2, 3, 7) Triangle Group, and Some Other Examples
This work studies the genus-1 curves associated with the congruence subgroups Γ0(3), Γ1(3) and compute the rational map of degree 28 of the covering of these curves, which is analogous to a Shimura curve associated with quaternion algebras over other cyclic cubic fields.
Shimura Curve Computations
Some methods for computing equations for certain Shimura curves, natural maps between them, and special points on them are given, and a list of open questions that may point the way to further computational investigation of these curves are illustrated.
REGULAR HONEYCOMBS IN HYPERBOLIC SPACE
made a study of honeycombs whose cells are equal regular polytopes in spaces of positive, zero, and negative curvature. The spherical and Euclidean honeycombs had already been described by Schlaf li
The Eightfold Way MSRI Publications
We give a detailed proof of Hirzebruch’s remarkable result that the symmetric Hilbert modular surface of level √ 7 for Q( √ 7) is PSL2(F7)equivariantly isomorphic to the complex projective plane. We