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

Building on techniques recently introduced by the second author, and further developed first we show that a positive integer $N$ may be rigorously 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 previous best known result factor of $(\log \log N)^{3/5}$.