Factorization of numbers with truncated Gauss sums at rational arguments

Abstract

Factorization of numbers with the help of Gauss sums relies on an intimate relationship between the maxima of these functions and the factors. Indeed, when we restrict ourselves to integer arguments of the Gauss sum we profit from a one-to-one relationship. As a result the identification of factors by the maxima is unique. However, for non-integer arguments such as rational numbers this powerful instrument to find factors breaks down. We develop new strategies for factoring numbers using Gauss sums at rational arguments. This approach may find application in a recent suggestion to factor numbers using an light interferometer [V. Tamma et al., J. Mod. Opt. in this volume] discussed in this issue.