On the Distribution of Witnesses in the Miller-Rabin Test

TL;DR

This paper demonstrates that Miller-Rabin witnesses are uniformly distributed in the unit interval by analyzing exponential sums, providing insights into their distribution properties.

Contribution

It establishes the equidistribution of Miller-Rabin witnesses using exponential sum techniques, a novel approach in understanding their distribution.

Findings

Witnesses are equidistributed in the unit interval

Exponential sums exhibit cancellation, indicating uniformity

Provides a new analytical method for distribution analysis

Abstract

We show that the set of normalized Miller-Rabin witnesses becomes equidistributed in the unit interval. This will be done by exhibiting cancellation in certain exponential sums.