The hardness of computing an eigenform
Number Theory
2007-08-13 v2
Abstract
In this article, we give evidence that computing Fourier coefficients of the Hecke eigenforms for composite indices is no easier than factoring integers. In particular, we show that the existence of a polynomial time algorithm that, given n, computes the n-th Fourier coefficient of a (fixed) Hecke eigenform implies that we can factor most RSA moduli (numbers that are products of two distinct primes) in polynomial time.
Cite
@article{arxiv.0708.1192,
title = {The hardness of computing an eigenform},
author = {Eric Bach and Denis Charles},
journal= {arXiv preprint arXiv:0708.1192},
year = {2007}
}
Comments
5 Pages (corrected a typo in statement of Theorem 2.1)