Elementary computation of the Jones polynomials for Torus links modulo primes.

We present simple congruences modulo p of the Jones polynomial for the torus link T (p , λ) , where p is a prime number and λ is a nonzero integer. These congruences are expressed in terms of Chebyshev polynomials and quantum numbers. The approach makes elementary use of the Kauffman bracket and does not require any representation theory. [ABSTRACT FROM AUTHOR]