An explicit formula for the Mahler measure of a family of 3 -variable polynomials

Chris J. Smyth

Journal de théorie des nombres de Bordeaux (2002)

  • Volume: 14, Issue: 2, page 683-700
  • ISSN: 1246-7405

Abstract

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An explicit formula for the Mahler measure of the 3 -variable Laurent polynomial a + b x - 1 + c y + ( a + b x + c y ) z is given, in terms of dilogarithms and trilogarithms.

How to cite

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Smyth, Chris J.. "An explicit formula for the Mahler measure of a family of $3$-variable polynomials." Journal de théorie des nombres de Bordeaux 14.2 (2002): 683-700. <http://eudml.org/doc/248892>.

@article{Smyth2002,
abstract = {An explicit formula for the Mahler measure of the $3$-variable Laurent polynomial $a + bx^\{-1\} + cy + (a + bx + cy)z$ is given, in terms of dilogarithms and trilogarithms.},
author = {Smyth, Chris J.},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {Mahler's measure; polylogarithm},
language = {eng},
number = {2},
pages = {683-700},
publisher = {Université Bordeaux I},
title = {An explicit formula for the Mahler measure of a family of $3$-variable polynomials},
url = {http://eudml.org/doc/248892},
volume = {14},
year = {2002},
}

TY - JOUR
AU - Smyth, Chris J.
TI - An explicit formula for the Mahler measure of a family of $3$-variable polynomials
JO - Journal de théorie des nombres de Bordeaux
PY - 2002
PB - Université Bordeaux I
VL - 14
IS - 2
SP - 683
EP - 700
AB - An explicit formula for the Mahler measure of the $3$-variable Laurent polynomial $a + bx^{-1} + cy + (a + bx + cy)z$ is given, in terms of dilogarithms and trilogarithms.
LA - eng
KW - Mahler's measure; polylogarithm
UR - http://eudml.org/doc/248892
ER -

References

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  9. [RV] F. Rodriguez Villegas, Modular Mahler measures. I, Topics in number theory (University Park, PA, 1997), 17-48, Math. Appl., 467, Kluwer Acad. Publ., Dordrecht, 1999. Zbl0980.11026MR1691309
  10. [Sc] A. Schinzel, Polynomials with Special Regard to Reducibility. With an appendix by Umberto Zannier. Encyclopedia of Mathematics and its Applications, 77, Cambridge University Press, Cambridge, 2000. Zbl0956.12001MR1770638
  11. [Sm] C.J. Smyth, On measures of polynomials in several variables. Bull. Austral. Math. Soc. Ser. A23 (1981), 49-63. Corrigendum (with G. Myerson): Bull. Austral. Math. Soc. Ser. A26 (1982), 317-319. Zbl0442.10034MR615132
  12. [Z] D. Zagier, The Bloch- Wigner-Ramakrishnan polylogarithm function. Math. Ann.286 (1990), 613-624. Zbl0698.33001MR1032949

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