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CALCULATING POWER INTEGRAL BASES IN SOME QUARTIC FIELDS CORRESPONDING TO MONOGENIC FAMILIES OF POLYNOMIALS
Keywords:
monogenity, power integral basis, quartic fields, Thue equationsDOI:
https://doi.org/10.17654/0972555525006Abstract
Harrington and Jones characterized monogenity of four new parametric families of quartic polynomials with various Galois groups. A short time later Voutier added a cyclic family. In this note, we intend to describe all generators of power integral bases in the number fields generated by a root of the monogenic polynomials.
Received: November 6, 2024
Revised: November 24, 2024
Accepted: December 5, 2024
References
I. Gaal, Diophantine equations and power integral bases, Theory and Algorithms, 2nd ed., Birkhauser, Boston, 2019.
I. Gaal, A. Petho and M. Pohst, On the resolution of index form equations in quartic number fields, J. Symbolic Comput. 16 (1993), 563-584.
I. Gaal, A. Petho and M. Pohst, Simultaneous representation of integers by a pair of ternary quadratic forms - with an application to index form equations in quartic number fields, J. Number Theory 57 (1996), 90-104.
J. Harrington and L. Jones, Monogenic quartic polynomials and their Galois groups, Bull. Aust. Math. Soc. (First published online 2024), page 1 of 16. doi:10.1017/S000497272400073X.
L. J. Mordell, Diophantine Equations, Academic Press, New York, London, 1969.
P. Voutier, A family of cyclic quartic monogenic polynomials, 2024. arXiv:2405.20288v2.
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