11/21/2007, 06:20 PM

Yes, they converge very rapidly. The fixed points increase by approximately 2*pi*I as we move away from the real line, so they form an arithmetic sequence to a first approximation. Therefore, they'll converge about as fast as the partial sums of the zeta function. So yes, we shouldn't need very many fixed points to calculate the coefficients of the rational numbers, though I haven't bothered to figure out if some minimum number of fixed points would suffice for all sums.

My main interest in calculating 100,000 fixed points was to generate continued fractions for each sum, and try to use those to provide strong numerical evidence that the infinite sums indeed converge on rational numbers.

My main interest in calculating 100,000 fixed points was to generate continued fractions for each sum, and try to use those to provide strong numerical evidence that the infinite sums indeed converge on rational numbers.

~ Jay Daniel Fox