Voronoi summation formulae and multiplicative functions on permutations

TL;DR

This paper develops a Tauberian theorem for Voronoi summation of divergent series and applies it to study the average behavior of multiplicative functions on random permutations.

Contribution

It introduces a new Tauberian theorem for Voronoi summation and uses it to analyze multiplicative functions in permutation groups.

Findings

Established a remainder estimate for Voronoi summation.

Derived mean value formulas for multiplicative functions on permutations.

Connected summability methods with permutation function analysis.

Abstract

We prove a Tauberian theorem for the Voronoi summation method of divergent series with an estimate of the remainder term. The results on the Voronoi summability are then applied to analyze the mean values of multiplicative functions on random permutations.