Topic
Klein quartic
About: Klein quartic is a research topic. Over the lifetime, 151 publications have been published within this topic receiving 2672 citations.
Papers published on a yearly basis
Papers
TL;DR: In this paper, the algebraic classification of non-euclidean plane crystallographic groups with compact quotient space was studied, including those which contain orientation-reversing reflections and glide-reflections.
Abstract: This paper deals with the algebraic classification of non-euclidean plane crystallographic groups (NEC groups, for short) with compact quotient space. The groups considered are the discrete groups of motions of the Lobatschewsky or hyperbolic plane, including those which contain orientation-reversing reflections and glide-reflections. The corresponding problem for Fuchsian groups, which contain only orientable transformations, is essentially solved in the work of Fricke and Klein (6).
215 citations
1 Jan 1999
TL;DR: In this article, a laterally opening hollow housing or truck is provided with a motor rotor having a horizontal shaft, and drive means are interposed between the motor shaft and running gear.
Abstract: A toy or model vehicle wherein a laterally opening hollow housing or truck is provided with a motor rotor having a horizontal shaft, and drive means are interposed between the motor shaft and running gear.
160 citations
TL;DR: In this paper, a nonabelian descent argument involving the simple group of order 168 reduces the problem to the determination of the set of rational points on a finite set of twists of the Klein quartic curve X.
Abstract: We find the primitive integer solutions to x2+y3=z7. A nonabelian descent argument involving the simple group of order 168 reduces the problem to the determination of the set of rational points on a finite set of twists of the Klein quartic curve X. To restrict the set of relevant twists, we exploit the isomorphism between X and the modular curve X(7) and use modularity of elliptic curves and level lowering. This leaves 10 genus 3 curves, whose rational points are found by a combination of methods
97 citations
TL;DR: In this paper, a nonabelian descent argument involving the simple group of order 168 was used to find the rational points on a finite set of twists of the Klein quartic curve X. This leaves 10 genus-3 curves whose rational points are found by a combination of methods.
Abstract: We find the primitive integer solutions to x^2+y^3=z^7. A nonabelian descent argument involving the simple group of order 168 reduces the problem to the determination of the set of rational points on a finite set of twists of the Klein quartic curve X. To restrict the set of relevant twists, we exploit the isomorphism between X and the modular curve X(7), and use modularity of elliptic curves and level lowering. This leaves 10 genus-3 curves, whose rational points are found by a combination of methods.
94 citations
92 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 5 |
| 2020 | 1 |
| 2019 | 6 |
| 2018 | 7 |
| 2017 | 11 |
| 2016 | 8 |