/sci/ - Science & Math

>>11000543
It wouldn't matter if the individual sums converged or not, because the non-convergence of one could easily be cancelled by the non-convergence of the other, and you're still left showing the sum of sums must converge.
Which, is already known to converge for at least some b, as there are already an infinite amount of known solutions on the critical line.
You could then probably show that the individual sums converge for at least some b, but I haven't explored the requirements on b that would lead to guaranteed convergence.