Multiplicative Functions and a Taxonomy of Dirichlet Characters

TL;DR

This paper introduces a method for estimating sums of multiplicative functions combined with Dirichlet characters, and develops a classification of characters based on the size of these sums.

Contribution

It provides a novel estimation technique and a taxonomy of Dirichlet characters related to large sums of multiplicative functions.

Findings

New estimation method for sums of multiplicative functions with Dirichlet characters

Taxonomy classifying characters based on sum size

Identification of characters leading to large sums

Abstract

A method of estimating sums of multiplicative functions braided with Dirichlet characters is demonstrated, leading to a taxonomy of the characters for which such sums are large.