We provide an alternative proof of the classical single-term asymptotics for
Toeplitz determinants whose symbols possess Fisher-Hartwig singularities. We
also relax the smoothness conditions on the regular part of the symbols and
obtain an estimate for the error term in the asymptotics. Our proof is based on
the Riemann-Hilbert analysis of the related systems of orthogonal polynomials
and on differential identities for Toeplitz determinants. The result discussed
in this paper is crucial for the proof of the asymptotics in the general case
of Fisher-Hartwig singularities and extensions to Hankel and Toeplitz+Hankel
determinants in [15].
