Volume 5 (2005)

Download this article
For screen
For printing
Recent Issues

Volume 13 (2013)
Issue 1 1–624
Issue 2 625–1241
Issue 3 1243–1856
Issue 4 1857–

Volume 12 (2012) 1–4

Volume 11 (2011) 1–5

Volume 10 (2010) 1–4

Volume 9 (2009) 1–4

Volume 8 (2008) 1–4

Volume 7 (2007)

Volume 6 (2006)

Volume 5 (2005)

Volume 4 (2004)

Volume 3 (2003)

Volume 2 (2002)

Volume 1 (2001)

The Journal
About the Journal
Editorial Board
Editorial Interests
Author Index
Editorial procedure
Submission Guidelines
Submission Page
Author copyright form
Subscriptions
Contacts
G&T Publications
GTP Author Index

On the Mahler measure of Jones polynomials under twisting

Abhijit Champanerkar and Ilya Kofman

Algebraic & Geometric Topology 5 (2005) 1–22

DOI: 10.2140/agt.2005.5.1

Bibliography
1 D W Boyd, F Rodriguez-Villegas, Mahler's measure and the dilogarithm I, Canad. J. Math. 54 (2002) 468–492 MR1900760
2 D Boyd, F Rodriguez-Villegas, N Dunfield, Mahler's measure and the dilogarithm II arXiv:math.NT/0308041
3 A Champanerkar, I Kofman, E Patterson, The next simplest hyperbolic knots, J. Knot Theory Ramifications 13 (2004) 965–987 MR2101238
4 S C Chang, R Shrock, Zeros of Jones polynomials for families of knots and links, Phys. A 301 (2001) 196–218 MR1874776
5 O T Dasbach, X S Lin, A volumish theorem for the Jones polynomial of alternating knots, Pacific J. Math. 231 (2007) 279–291 MR2346497
6 F M Goodman, P de la Harpe, V F R Jones, Coxeter graphs and towers of algebras, Mathematical Sciences Research Institute Publications 14, Springer (1989) MR999799
7 S Gukov, Three-dimensional quantum gravity, Chern–Simons theory, and the A–polynomial, Comm. Math. Phys. 255 (2005) 577–627 MR2134725
8 X Jin, F Zhang, Zeros of the Jones polynomials for families of pretzel links, Phys. A 328 (2003) 391–408 MR2013217
9 V F R Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math. (2) 126 (1987) 335–388 MR908150
10 L H Kauffman, An invariant of regular isotopy, Trans. Amer. Math. Soc. 318 (1990) 417–471 MR958895
11 A Kawauchi, A survey of knot theory, Birkhäuser Verlag (1996) MR1417494 Translated and revised from the 1990 Japanese original by the author
12 R Kirby, P Melvin, The 3–manifold invariants of Witten and Reshetikhin–Turaev for sl(2,C), Invent. Math. 105 (1991) 473–545 MR1117149
13 M Lackenby, The volume of hyperbolic alternating link complements, Proc. London Math. Soc. (3) 88 (2004) 204–224 MR2018964 With an appendix by Ian Agol and Dylan Thurston
14 R A Landvoy, The Jones polynomial of pretzel knots and links, Topology Appl. 83 (1998) 135–147 MR1606488
15 W M Lawton, A problem of Boyd concerning geometric means of polynomials, J. Number Theory 16 (1983) 356–362 MR707608
16 X S Lin, Zeros of the Jones polynomial
17 H Murakami, J Murakami, The colored Jones polynomials and the simplicial volume of a knot, Acta Math. 186 (2001) 85–104 MR1828373
18 V V Prasolov, A B Sossinsky, Knots, links, braids and 3–manifolds, Translations of Mathematical Monographs 154, American Mathematical Society (1997) MR1414898 An introduction to the new invariants in low-dimensional topology, Translated from the Russian manuscript by Sossinsky [Sosinskiĭ]
19 A Schinzel, The Mahler measure of polynomials, from: "Number theory and its applications (Ankara, 1996)", Lecture Notes in Pure and Appl. Math. 204, Dekker (1999) 171–183 MR1661667
20 A Schinzel, Polynomials with special regard to reducibility, Encyclopedia of Mathematics and its Applications 77, Cambridge University Press (2000) MR1770638 With an appendix by Umberto Zannier
21 D S Silver, S G Williams, Mahler measure of Alexander polynomials, J. London Math. Soc. (2) 69 (2004) 767–782 MR2050045
22 N P Skoruppa, Heights, graduate course, Bordeaux (1999)
23 C J Smyth, On the product of the conjugates outside the unit circle of an algebraic integer, Bull. London Math. Soc. 3 (1971) 169–175 MR0289451
24 H Wenzl, Hecke algebras of type An and subfactors, Invent. Math. 92 (1988) 349–383 MR936086
25 F Y Wu, J Wang, Zeroes of the Jones polynomial, Phys. A 296 (2001) 483–494 MR1840867
26 Y Yokota, Twisting formulas of the Jones polynomial, Math. Proc. Cambridge Philos. Soc. 110 (1991) 473–482 MR1120482