A log-log speedup for exponent one-fifth deterministic integer factorisation

Building on techniques recently introduced by the second author, and further developed by the first author, we show that a positive integer N may be rigorously and deterministically factored into primes in at most \[ O\left ( \frac {N^{1/5} \log ^{16/5} N}{(\log \log N)^{3/5}}\right ) \] bit operations. This improves on the previous best known result by a factor of (\log \log N)^{3/5}.