Proof of the volume conjecture for Whitehead doubles of a family of torus knots (Q2465554)

The paper computes the first two leading order terms in the asymptotic expansion of \(\log | J_{K,N}(e^{2\pi\sqrt{-1}/N})|\) as \(N\rightarrow \infty\), where \(K\) is a Whitehead double of a non trivial torus knot \(T(p,q)\) with \(q=2\), and \(J_{K,N}\) the (suitably normalized) Jones polynomial of \(K\) with color \(N\). In particular, the result confirms the Kashaev-Murakami-Murakami volume conjecture. A method to compute the colored Jones polynomials of more general satellite knots is used. Technical problems related to a corresponding extension of the results obtained are discussed at the end of the paper.