Randomness of character sums modulo $m$

TL;DR

This paper demonstrates that certain real character sums are uniformly distributed across residue classes modulo m by employing a probabilistic model based on random walks on the additive group.

Contribution

It introduces a novel probabilistic approach using random walks to analyze the distribution of character sums modulo m.

Findings

Values of specific real character sums are uniformly distributed in residue classes.

The probabilistic model effectively predicts distribution patterns.

Provides new insights into the behavior of character sums in modular arithmetic.

Abstract

Using a probabilistic model, based on random walks on the additive group $\mathbb{Z}/m\mathbb{Z}$, we prove that the values of certain real character sums are uniformly distributed in residue classes modulo $m$.