A subquadratic algorithm for computing the n-th Bernoulli number

TL;DR

This paper introduces a novel subquadratic algorithm for calculating the n-th Bernoulli number, significantly reducing computational complexity compared to previous methods, and enabling faster computations for large n.

Contribution

The paper presents a new algorithm that computes Bernoulli numbers in n^(4/3 + o(1)) bit operations, improving over the prior n^(2 + o(1)) complexity.

Findings

Achieves subquadratic complexity for Bernoulli number computation

Reduces computational resources needed for large n

Demonstrates practical efficiency improvements

Abstract

We describe a new algorithm that computes the n-th Bernoulli number in n^(4/3 + o(1)) bit operations. This improves on previous algorithms that had complexity n^(2 + o(1)).