Nonreciprocal algebraic numbers of small measure
Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 4, pp. 693-697
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The main result of this paper implies that for every positive integer $d\geqslant 2$ there are at least $(d-3)^2/2$ nonconjugate algebraic numbers which have their Mahler measures lying in the interval $(1,2)$. These algebraic numbers are constructed as roots of certain nonreciprocal quadrinomials.
The main result of this paper implies that for every positive integer $d\geqslant 2$ there are at least $(d-3)^2/2$ nonconjugate algebraic numbers which have their Mahler measures lying in the interval $(1,2)$. These algebraic numbers are constructed as roots of certain nonreciprocal quadrinomials.
Classification :
11R06, 11R09
Keywords: Mahler measure; quadrinomials; irreducibility; nonreciprocal numbers
Keywords: Mahler measure; quadrinomials; irreducibility; nonreciprocal numbers
@article{CMUC_2004_45_4_a9,
author = {Dubickas, Art\={u}ras},
title = {Nonreciprocal algebraic numbers of small measure},
journal = {Commentationes Mathematicae Universitatis Carolinae},
pages = {693--697},
year = {2004},
volume = {45},
number = {4},
mrnumber = {2103084},
zbl = {1127.11070},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMUC_2004_45_4_a9/}
}
Dubickas, Artūras. Nonreciprocal algebraic numbers of small measure. Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 4, pp. 693-697. http://geodesic.mathdoc.fr/item/CMUC_2004_45_4_a9/