Index form equations in quintic fields

István Gaál, Kálmán Győry

Type: Article

Publication Date: 1999-01-01

Citations: 34

DOI: https://doi.org/10.4064/aa-89-4-379-396

Abstract

The problem of determining power integral bases in algebraic number fields is equivalent to solving the corresponding index form equations. As is known (cf. Győry [25]), every index form equation can be reduced to an equation system consisting of unit equ

Locations

Acta Arithmetica - View - PDF

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Action	Title	Year	Authors
+ PDF Chat	On Indices of Septic Number Fields Defined by Trinomials x7 + ax + b	2023	Lhoussain El Fadil
+ PDF Chat	Integral Bases and Monogenity of Pure Number Fields with Non-Square Free Parameters up to Degree 9	2023	Lhoussain El Fadil István Gaál
+ PDF Chat	Power integral bases in cubic and quartic extensions of real quadratic fields	2019	István Gaál László Remete
+	Power Integral Bases in Cubic Relative Extensions	2001	István Gaál
+	Power Bases for 2-Power Cyclotomic Fields	2001	Leanne Robertson
+ PDF Chat	ON NONMONOGENIC NUMBER FIELDS DEFINED BY TRINOMIALS OF TYPE xn+axm+b	2023	Hamid Ben Yakkou
+ PDF Chat	Non-monogenity in a family of octic fields	2017	István Gaál László Remete
+	Calculating generators of power integral bases in pure sextic fields	2023	István Gaál
+ PDF Chat	Index form equations in sextic fields: a hard computation	2004	Yuri Bilu István Gaál Kálmán Győry
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Works Cited by This (24)

Action	Title	Year	Authors
+	Application of thue equations to computing power integral bases in algebraic number fields	1996	István Gaál
+	A Course in Computational Algebraic Number Theory	1993	Henri Cohen
+ PDF Chat	Decomposable form equations	1988	Jan‐Hendrik Evertse K. Győry
+	POWER INTEGRAL BASES IN COMPOSITS OF NUMBER FIELDS	1998	Ga ́ Al
+ PDF Chat	Computing all power integral bases in orders of totally real cyclic sextic number fields	1996	István Gaál
+	Logarithmic forms and group varieties.	1993	A. Baker Gisbert Wüstholz
+	Solving Discriminant Form Equations Via Unit Equations	1996	Nigel P. Smart
+ PDF Chat	Computing all power integral bases of cubic fields	1989	István Gaál Ν. Schulte
+	On the Resolution of Index Form Equations in Sextic Fields with an Imaginary Quadratic Subfield	1996	István Gaál Michael Pohst
+	Solving Index Form Equations in Fields of Degree 9 with Cubic Subfields	2000	István Gaál