On Lehmer’s question for integer-valued polynomials
Berend Ringeling1
1 Department of Mathematics, IMAPP Radboud University, PO Box 9010 6500 GL Nijmegen, Netherlands
Journal de théorie des nombres de Bordeaux, Tome 36 (2024) no. 2, pp. 527-536.

Nous répondons à une question de type Lehmer sur la mesure de Mahler des polynômes à valeurs entières.

We solve a Lehmer-type question about the Mahler measure of integer-valued polynomials.

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DOI : 10.5802/jtnb.1287
Classification : 11R06, 11R09
Mots clés : Mahler measure, polynomials, asymptotics
Berend Ringeling 1

1 Department of Mathematics, IMAPP Radboud University, PO Box 9010 6500 GL Nijmegen, Netherlands
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Berend Ringeling. On Lehmer’s question for integer-valued polynomials. Journal de théorie des nombres de Bordeaux, Tome 36 (2024) no. 2, pp. 527-536. doi : 10.5802/jtnb.1287. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1287/

[1] François Brunault; Wadim Zudilin Many variations of Mahler measures: a lasting symphony, Australian Mathematical Society Lecture Series, 28, Cambridge University Press, 2020, xv+167 pages | DOI | Zbl

[2] Keith Conrad Irreducibility of x n -x-1 (unpublished note, available at https://kconrad.math.uconn.edu/blurbs/ringtheory/irredselmerpoly.pdf)

[3] Wilhelm Ljunggren On the irreducibility of certain trinomials and quadrinomials, Math. Scand., Volume 8 (1960), pp. 65-70 | DOI | Zbl

[4] George Pólya; Gabor Szegő Problems and theorems in analysis. II. Theory of functions, zeros, polynomials, determinants, number theory, geometry, Classics in Mathematics, Springer, 1998, xii+392 pages (translated from German by C. E. Billigheimer, reprint of the 1976 English translation) | Zbl

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