A Proof of Merca's Conjectures on Sums of Odd Divisor Functions
Number Theory
2021-07-22 v2
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 -gonal numbers. Extending Merca's work, we complete the proof of these conjectures.
Cite
@article{arxiv.2107.07637,
title = {A Proof of Merca's Conjectures on Sums of Odd Divisor Functions},
author = {Kaya Lakein and Anne Larsen},
journal= {arXiv preprint arXiv:2107.07637},
year = {2021}
}
Comments
This revision includes further commentary about Merca's conjectures. This paper will appear in the Bulletin of the Australian Mathematical Society