# Nonreciprocal algebraic numbers of small measure

Commentationes Mathematicae Universitatis Carolinae (2004)

- Volume: 45, Issue: 4, page 693-697
- ISSN: 0010-2628

## Access Full Article

top## Abstract

top## How to cite

topDubickas, Artūras. "Nonreciprocal algebraic numbers of small measure." Commentationes Mathematicae Universitatis Carolinae 45.4 (2004): 693-697. <http://eudml.org/doc/249374>.

@article{Dubickas2004,

abstract = {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.},

author = {Dubickas, Artūras},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {Mahler measure; quadrinomials; irreducibility; nonreciprocal numbers; Mahler measure; quadrinomials; irreducibility; nonreciprocal numbers},

language = {eng},

number = {4},

pages = {693-697},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Nonreciprocal algebraic numbers of small measure},

url = {http://eudml.org/doc/249374},

volume = {45},

year = {2004},

}

TY - JOUR

AU - Dubickas, Artūras

TI - Nonreciprocal algebraic numbers of small measure

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2004

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 45

IS - 4

SP - 693

EP - 697

AB - 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.

LA - eng

KW - Mahler measure; quadrinomials; irreducibility; nonreciprocal numbers; Mahler measure; quadrinomials; irreducibility; nonreciprocal numbers

UR - http://eudml.org/doc/249374

ER -

## References

top- Boyd D.W., Perron units which are not Mahler measures, Ergodic Theory Dynam. Systems 6 (1986), 485-488. (1986) Zbl0591.12003MR0873427
- Boyd D.W., Montgomery H.L., Cyclotomic Partitions, Number Theory (R.A. Mollin, ed.), Walter de Gruyter, Berlin, 1990, pp.7-25. Zbl0697.10040MR1106647
- Chern S.J., Vaaler J.D., The distribution of values of Mahler's measure, J. Reine Angew. Math. 540 (2001), 1-47. (2001) Zbl0986.11017MR1868596
- Dixon J.D., Dubickas A., The values of Mahler measures, Mathematika, to appear. Zbl1107.11044MR2220217
- Dubickas A., Algebraic conjugates outside the unit circle, New Trends in Probability and Statistics Vol. 4: Analytic and Probabilistic Methods in Number Theory (A. Laurinčikas et al., eds.), Palanga, 1996, TEV Vilnius, VSP Utrecht, 1997, pp.11-21. Zbl0923.11146MR1653596
- Dubickas A., Konyagin S.V., On the number of polynomials of bounded measure, Acta Arith. 86 (1998), 325-342. (1998) Zbl0926.11080MR1659085
- Ljunggren W., On the irreducibility of certain trinomials and quadrinomials, Math. Scand. 8 (1960), 65-70. (1960) Zbl0095.01305MR0124313
- Mignotte M., Sur les nombres algébriques de petite mesure, Comité des Travaux Historiques et Scientifiques: Bul. Sec. Sci. 3 (1981), 65-80. (1981) Zbl0467.12008MR0638732
- Mignotte M., On algebraic integers of small measure, Topics in Classical Number Theory, Budapest, 1981, vol. II (G. Halász, ed.), Colloq. Math. Soc. János Bolyai 34 (1984), 1069-1077. (1984) Zbl0543.12002MR0781176
- Schinzel A., Polynomials with Special Regard to Reducibility, Encyclopedia of Mathematics and its Applications 77, Cambridge University Press, 2000. Zbl0956.12001MR1770638
- Smyth C.J., On the product of the conjugates outside the unit circle of an algebraic integer, Bull. London Math. Soc. 3 (1971), 169-175. (1971) Zbl0235.12003MR0289451
- Smyth C.J., Topics in the theory of numbers, Ph.D. Thesis, University of Cambridge, 1972.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.