A Proof of Merca's Conjectures on Sums of Odd Divisor Functions

Abstract

In a recent paper, Merca posed three conjectures on congruences for specific convolutions of a sum of odd divisor functions with a generating function for generalized $m$-gonal numbers. Extending Merca's work, we complete the proof of these conjectures.

This revision includes further commentary about Merca's conjectures. This paper will appear in the Bulletin of the Australian Mathematical Society