Summation properties of the and Li constants

We find new summatory and other properties of the constants η j entering the Laurent expansion of the logarithmic derivative of the Riemann zeta function about s = 1 . We relate these constants to other coefficients and functions appearing in the theory of the zeta function. In particular, connections to the Li equivalence of the Riemann hypothesis are discussed and quantitatively developed. The validity of the Riemann hypothesis is reduced to the condition of the sublinear order of a certain alternating binomial sum.