## Title data

Hutz, Benjamin ; Stoll, Michael:

**Smallest representatives of SL(2,ℤ)-orbits of binary forms and endomorphisms of ℙ¹.**

*In:* Acta Arithmetica.
Vol. 189
(2019)
Issue 3
.
- pp. 283-308.

ISSN 0065-1036

DOI: https://doi.org/10.4064/aa180618-9-12

## Abstract in another language

We develop an algorithm that determines, for a given squarefree binary form F with real coefficients, a smallest representative of its orbit under SL(2,Z), either with respect to the Euclidean norm or with respect to the maximum norm of the coefficient vector. This is based on earlier work of Cremona and Stoll (2003). We then generalize our approach so that it also applies to the problem of finding an integral representative of smallest height in the PGL(2,Q) conjugacy class of an endomorphism of the projective line. Having a small model of such an endomorphism is useful for various computations.

## Further data

Item Type: | Article in a journal |
---|---|

Refereed: | Yes |

Keywords: | binary form; dynamical system; reduced; minimal model |

Subject classification: | 2010 Mathematics Subject Classification: 37P05, 37P45, 11C08, 11Y99 |

Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II > Chair Mathematics II - Univ.-Prof. Dr. Michael Stoll |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 19 Aug 2019 08:07 |

Last Modified: | 19 Aug 2019 08:07 |

URI: | https://eref.uni-bayreuth.de/id/eprint/51925 |