Recurrence Relations and Asymptotics of Colored Jones Polynomials-Reference-Cited by-同舟云学术

Recurrence Relations and Asymptotics of Colored Jones Polynomials

Published:2021-11 Issue:11 Volume:42 Page:2580-2595
ISSN:1995-0802
Container-title:Lobachevskii Journal of Mathematics
language:en
Short-container-title:Lobachevskii J Math

Author:

Aptekarev A. I.,Dudnikova T. V.,Tulyakov D. N.

Abstract

Abstract We consider

$$q$$

-difference equations for colored Jones polynomials. These sequences of polynomials are invariants for the knots and their asymptotics plays an important role in the famous volume conjecture for the complement of the knot to the

$$3$$

d sphere. We give an introduction to the theory of hyperbolic volume of the knots complements and study the asymptotics of the solutions of

$$q$$

-recurrence relations of high order.

Publisher

Pleiades Publishing Ltd

Subject

General Mathematics

Link

https://link.springer.com/content/pdf/10.1134/S1995080221110056.pdf

Reference63 articles.

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3. A. I. Aptekarev and D. N. Tulyakov, ‘‘Asymptotics of Meixner polynomials and Christoffel–Darboux kernels,’’ Trans. Mosc. Math. Soc. 73, 67–106 (2012).

4. A. I. Aptekarev and D. N. Tulyakov, ‘‘The leading term of the Plancherel–Rotach asymptotic formula for solutions of recurrence relations,’’ Sb. Math. 205, 1696–1719 (2014).

5. A. I. Aptekarev and D. N. Tulyakov, ‘‘Asymptotical basis of solutions of $$q$$-recurrence relations outside of the zone of clustering eigenvalues,’’ KIAM Preprint No. 159 (Keldysh Inst. Appl. Math., Moscow, 2018). https://doi.org/10.20948/prepr-2018-159

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