Reidemeister torsion is a numerical invariant for a finite cell complex with a linear representation of the fundamental group.
In this talk we consider this invariant for a homology 3-sphere M with an SL(2;C)-irreducible representation.
We assume that the SL(2;C)-character variety of M is finite set. Then we can define a polynomial whose zeros are values of Reidemeister torsions.
For Brieskorn homology 3-spheres and the manifolds obtained by 1/n-surgery along the figure eight knot, we can give explicit formulas by using Chebyshev polynomials of the first and second types.
Further we discuss the relation between this polynomial and the SL(2;C)-Casson invariant.
This is part of joint works with Anh Tran.