Hittmeir recently presented a deterministic algorithm that provably computes the prime factorisation of a positive integer $N$ in $N^{2/9+o(1)}$ bit operations. Prior to this breakthrough, the best known complexity bound for this problem was $N^{1/4+o(1)}$, a result going back to the 1970s. In this paper we push Hittmeir's techniques further, obtaining a rigorous, deterministic factoring algorithm with complexity $N^{1/5+o(1)}$.

翻译：Hittmeir最近提出了一个确定性算法,该算法以美元计算正整数正整数美元($N ⁇ 2/9+o(1)}美元)的起始因数。在取得这一突破之前,这一问题最已知的复杂程度是美元1/4+o(1)}美元,这一结果可以追溯到1970年代。在本文中,我们进一步推动赫特梅尔的技术,获得一种精确的确定性因数算法,其复杂性为$N ⁇ 1/5+o(1)}。