@article{808967bed3834b5288c24d7787a6874b,
title = "From colored Jones invariants to logarithmic invariants",
abstract = "In this paper, we express the logarithmic invariant of knots in terms of derivatives of the colored Jones invariants. Logarithmic invariant is defined by using the Jacobson radicals of the restricted quantum group Ūξ (sl2) where ξ is a root of unity. We also propose a version of the volume conjecture stating a relation between the logarithmic invariants and the hyperbolic volumes of the cone manifolds along a knot, which is proved for the figure-eight knot.",
keywords = "Hyperbolic volume, Knot theory, Quantum group",
author = "Jun Murakami",
note = "Funding Information: I would like to thank Gregor Masbaum for valuable discussion. This research is partially supported by the Grant-in-Aid for Scientific Research (B) (25287014), Exploratory Research (25610022) of Japan Society for the Promotion of Science, and the Erwin Schr{\"o}dinger Institute for Mathematical Physics (ESI) in Vienna. Publisher Copyright: {\textcopyright} 2018 International Academic Printing Co. Ltd.. All rights reserved.",
year = "2018",
doi = "10.3836/tjm/1502179244",
language = "English",
volume = "41",
pages = "453--475",
journal = "Tokyo Journal of Mathematics",
issn = "0387-3870",
publisher = "Publication Committee for the Tokyo Journal of Mathematics",
number = "2",
}