On Ramanujan-type Congruences for Multiplicative Functions

TL;DR

This paper explores the existence and classification of Ramanujan-type congruences for multiplicative functions, inspired by recent links between divisor sums, overpartitions, and arithmetic progressions, expanding understanding in number theory.

Contribution

It introduces new classifications and insights into Ramanujan-type congruences within multiplicative functions, bridging additive and multiplicative number theory.

Findings

Identifies conditions for Ramanujan-type congruences in multiplicative functions

Classifies types of such congruences based on recent divisor sum and overpartition connections

Provides a framework for future research in number theory congruences

Abstract

The study of Ramanujan-type congruences for functions specific to additive number theory has a long and rich history. Motivated by recent connections between divisor sums and overpartitions via congruences in arithmetic progressions, we investigate the existence and classification of Ramanujan-type congruences for functions in multiplicative number theory.