On the number of parts of integer partitions lying in given residue classes

TL;DR

This paper uses Wright's Circle Method to derive an asymptotic formula for counting parts in integer partitions that belong to specific residue classes, advancing previous research in the area.

Contribution

It introduces a new asymptotic formula for parts in partitions within any arithmetic progression, improving upon earlier methods.

Findings

Derived an asymptotic formula for parts in residue classes

Extended previous results to more general arithmetic progressions

Enhanced understanding of partition structure in residue classes

Abstract

Improving upon previous work on the subject, we use Wright's Circle Method to derive an asymptotic formula for the number of parts in all partitions of an integer that are in any given arithmetic progression.