A note on the values of Mahler measure in quadratic fields
Canadian mathematical bulletin, Tome 68 (2025) no. 4, pp. 1267-1277
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In this note, we prove that quadratic algebraic integers, except for trivial cases, are not Mahler measures of algebraic integers and we also answer in negative the question of A. Schinzel [9] whether $1+\sqrt {17}$ is a Mahler measure of an algebraic number.
Mots-clés :
Mahler measure, quadratic algebraic numbers, polynomials
Dobrowolski, Edward; Wang, Yun. A note on the values of Mahler measure in quadratic fields. Canadian mathematical bulletin, Tome 68 (2025) no. 4, pp. 1267-1277. doi: 10.4153/S0008439525000451
@article{10_4153_S0008439525000451,
author = {Dobrowolski, Edward and Wang, Yun},
title = {A note on the values of {Mahler} measure in quadratic fields},
journal = {Canadian mathematical bulletin},
pages = {1267--1277},
year = {2025},
volume = {68},
number = {4},
doi = {10.4153/S0008439525000451},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439525000451/}
}
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