  The alternating zeta function zeta*(s) = 1 - 2^{-s} + 3^{-s} - ... is related
to the Riemann zeta function by the identity (1-2^{1-s})zeta(s) = zeta*(s). We
deduce the vanishing of zeta*(s) at each nonreal zero of the factor 1-2^{1-s}
without using the identity. Instead, we use a formula connecting the partial
sums of the series for zeta*(s) to Riemann sums for the integral of x^{-s} from
x=1 to x=2. We relate the proof to our earlier paper "The Riemann Hypothesis,
simple zeros, and the asymptotic convergence degree of improper Riemann sums,"
Proc. Amer. Math. Soc. 126 (1998) 1311-1314.
