# Essentially Optimal Sparse Polynomial Multiplication

arXiv: https://arxiv.org/abs/2001.11959 · HTML: https://mlsanity.com/paper/2001.11959/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2020.

## Built on by (most cited first, 1 of 1)

- [MechMath Agent Team: LLM Driven Agents for Mathematical Research](https://mlsanity.com/paper/2607.04394/) (2026)

## Abstract (arXiv)

We present a probabilistic algorithm to compute the product of two univariate sparse polynomials over a field with a number of bit operations that is quasi-linear in the size of the input and the output. Our algorithm works for any field of characteristic zero or larger than the degree. We mainly rely on sparse interpolation and on a new algorithm for verifying a sparse product that has also a quasi-linear time complexity. Using Kronecker substitution techniques we extend our result to the multivariate case.