The house of an algebraic integer is the maximum absolute value of its algebraic conjugates. Lower bounds for the house may be easier to prove than lower bounds for the height, as V. Dimitrov’s recent proof of the Schinzel–Zassenhaus conjecture suggests. We prove an analogue for the house of a recent conjecture by G. Rémond on lower bounds for the height in some radical extensions.
Lower bounds for the house in some radical extensions
Amoroso, Francesco
2024-01-01
Abstract
The house of an algebraic integer is the maximum absolute value of its algebraic conjugates. Lower bounds for the house may be easier to prove than lower bounds for the height, as V. Dimitrov’s recent proof of the Schinzel–Zassenhaus conjecture suggests. We prove an analogue for the house of a recent conjecture by G. Rémond on lower bounds for the height in some radical extensions.
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