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Quartic index form equations and monogenizations of quartic orders

Shabnam Akhtari

Vol. 1 (2022), No. 1, 57–72
Abstract

Some upper bounds for the number of monogenizations of quartic orders are established by considering certain classical Diophantine equations, namely index form equations in quartic number fields, and cubic and quartic Thue equations.

Keywords
monogenizations of a quartic order, index form equations, Thue equations
Mathematical Subject Classification
Primary: 11D25, 11D45, 11R04, 11R16
Milestones
Received: 18 March 2022
Revised: 22 June 2022
Accepted: 28 June 2022
Published: 26 October 2022
Authors
Shabnam Akhtari
Department of Mathematics
University of Oregon
Eugene, OR
United States