Volume conjecture and asymptotic expansion of q-series

研究成果: ジャーナルへの寄稿記事

17 引用 (Scopus)

抄録

We consider the "volume conjecture," which states that an asymptotic limit of Kashaev's invariant (or, the colored Jones type invariant) of knot K gives the hyperbolic volume of the complement of knot K. In the first part, we analytically study an asymptotic behavior of the invariant for the torus knot, and propose identities concerning an asymptotic expansion of q-series which reduces to the invariant with q being the N -th root of unity. This is a generalization of an identity recently studied by Zagier. In the second part, we show that "volume conjecture" is numerically supported for hyperbolic knots and links (knots up to 6-crossing, Whitehead link, and Borromean rings).

元の言語英語
ページ(範囲)319-337
ページ数19
ジャーナルExperimental Mathematics
12
発行部数3
DOI
出版物ステータス出版済み - 1 1 2003
外部発表Yes

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Q-series
Asymptotic Expansion
Knot
Invariant
Borromean rings
Hyperbolic Volume
Hyperbolic Knot
Torus knot
Asymptotic Limit
Roots of Unity
Complement
Asymptotic Behavior

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

これを引用

Volume conjecture and asymptotic expansion of q-series. / Hikami, Kazuhiro.

:: Experimental Mathematics, 巻 12, 番号 3, 01.01.2003, p. 319-337.

研究成果: ジャーナルへの寄稿記事

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