  We consider Conway polynomials of two-bridge links as Euler continuant
polynomials. As a consequence, we obtain new and elementary proofs of classical
Murasugi's 1958 alternating theorem and Hartley's 1979 trapezoidal theorem. We
give a modulo 2 congruence for links, which implies the classical Murasugi's
1971 congruence for knots. We also give sharp bounds for the coefficients of
Euler continuants and deduce bounds for the Alexander polynomials of two-bridge
links. These bounds improve and generalize those of Nakanishi Suketa'96. We
easily obtain some bounds for the roots of the Alexander polynomials of
two-bridge links. This is a partial answer to Hoste's conjecture on the roots
of Alexander polynomials of alternating knots.

Geometric Topology