| Title:
|
Nonreciprocal algebraic numbers of small measure (English) |
| Author:
|
Dubickas, Artūras |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
45 |
| Issue:
|
4 |
| Year:
|
2004 |
| Pages:
|
693-697 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Mahler measure |
| Keyword:
|
quadrinomials |
| Keyword:
|
irreducibility |
| Keyword:
|
nonreciprocal numbers |
| MSC:
|
11R06 |
| MSC:
|
11R09 |
| idZBL:
|
Zbl 1127.11070 |
| idMR:
|
MR2103084 |
| . |
| Date available:
|
2009-05-05T16:48:25Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119494 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Chern S.J., Vaaler J.D.: The distribution of values of Mahler's measure.J. Reine Angew. Math. 540 (2001), 1-47. Zbl 0986.11017, MR 1868596 |
| Reference:
|
[4] Dixon J.D., Dubickas A.: The values of Mahler measures.Mathematika, to appear. Zbl 1107.11044, MR 2220217 |
| Reference:
|
[5] 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. Zbl 0923.11146, MR 1653596 |
| Reference:
|
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| Reference:
|
[7] Ljunggren W.: On the irreducibility of certain trinomials and quadrinomials.Math. Scand. 8 (1960), 65-70. Zbl 0095.01305, MR 0124313 |
| Reference:
|
[8] Mignotte M.: Sur les nombres algébriques de petite mesure.Comité des Travaux Historiques et Scientifiques: Bul. Sec. Sci. 3 (1981), 65-80. Zbl 0467.12008, MR 0638732 |
| Reference:
|
[9] 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. Zbl 0543.12002, MR 0781176 |
| Reference:
|
[10] Schinzel A.: Polynomials with Special Regard to Reducibility.Encyclopedia of Mathematics and its Applications 77, Cambridge University Press, 2000. Zbl 0956.12001, MR 1770638 |
| Reference:
|
[11] 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. Zbl 0235.12003, MR 0289451 |
| Reference:
|
[12] Smyth C.J.: Topics in the theory of numbers.Ph.D. Thesis, University of Cambridge, 1972. |
| . |
