The Multiplicities of Root Number Functions

TL;DR

This paper develops an asymptotic formula for the multiplicities of the $q$th root number function in symmetric groups as $q$ increases, using character theory, number theory, and combinatorics.

Contribution

It introduces a novel asymptotic analysis of root number function multiplicities for symmetric groups as $q$ grows large.

Findings

Derived an asymptotic formula for multiplicities

Applied character theory, number theory, and combinatorics

Enhanced understanding of root number functions in symmetric groups

Abstract

We consider the $q$th root number function for the symmetric group. Our aim is to develop an asymptotic formula for the multiplicities of the $q$th root number function as $q$ tends to $\infty$. We use character theory, number theory and combinatorics.