### Abstract

We give considerable improvements of the previous bounds on the solutions of decomposable form equations. Further, we generalize and make more efficient our earlier method for solving such equations via unit equations. Some applications are also presented to polynomials and algebraic integers of given discriminant and to power integral bases of number fields.

Original language | English |
---|---|

Pages (from-to) | 1-31 |

Number of pages | 31 |

Journal | Publicationes Mathematicae |

Volume | 52 |

Issue number | 1 |

Publication status | Published - 1998 |

### Fingerprint

### Keywords

- Discriminant form and index form equations
- Norm form
- Polynomials and algebraic integers of given discriminant
- Power integral bases

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Publicationes Mathematicae*,

*52*(1), 1-31.

**Bounds for the solutions of decomposable form equations.** / Györy, K.

Research output: Contribution to journal › Article

*Publicationes Mathematicae*, vol. 52, no. 1, pp. 1-31.

}

TY - JOUR

T1 - Bounds for the solutions of decomposable form equations

AU - Györy, K.

PY - 1998

Y1 - 1998

N2 - We give considerable improvements of the previous bounds on the solutions of decomposable form equations. Further, we generalize and make more efficient our earlier method for solving such equations via unit equations. Some applications are also presented to polynomials and algebraic integers of given discriminant and to power integral bases of number fields.

AB - We give considerable improvements of the previous bounds on the solutions of decomposable form equations. Further, we generalize and make more efficient our earlier method for solving such equations via unit equations. Some applications are also presented to polynomials and algebraic integers of given discriminant and to power integral bases of number fields.

KW - Discriminant form and index form equations

KW - Norm form

KW - Polynomials and algebraic integers of given discriminant

KW - Power integral bases

UR - http://www.scopus.com/inward/record.url?scp=0039506324&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039506324&partnerID=8YFLogxK

M3 - Article

VL - 52

SP - 1

EP - 31

JO - Publicationes Mathematicae

JF - Publicationes Mathematicae

SN - 0033-3883

IS - 1

ER -