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 $$O\left(\frac{N^{1\mathrm{/}5}{\log }^{16\mathrm{/}5}N}{(\log \log N{)}^{3\mathrm{/}5}}\right)$$ bit operations. This improves on the previous best known result by a factor of $(\log \log N)^{3/5}$.