I think capitalization messed up the title here: It should be N^o(1)
Does this impact RSA in any way or those deterministic time methods are irrelevant (as in much too slow) for key breaking?
General Number Field Sieve is the fastest general-purpose algorithm for factoring huge numbers, and is what most record factorizations use (exceptions exist for special classes of numbers). It already meets the N^o(1) bound this purports to prove, but it does so non-deterministically. The main result here is that there also exists a deterministic factoring algorithm that meets roughly the same complexity bounds as GNFS.