Asymptotics of the number of partitions into p-cores and some trigonometric sums

TL;DR

This paper derives an asymptotic formula for counting partitions into p-cores and discovers related integer-valued trigonometric sums, advancing understanding in partition theory and trigonometric sum evaluation.

Contribution

It introduces a new asymptotic formula for partitions into p-cores and identifies novel integer-valued trigonometric sums, expanding theoretical knowledge.

Findings

Asymptotic formula for p-core partitions derived

Identification of integer-valued trigonometric sums

Enhanced understanding of partition asymptotics

Abstract

An asymptotic formula for the number of partitions into p-cores is derived. As a byproduct some integer valued trigonometric sums are found