English

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 mm-gonal numbers. Extending Merca's work, we complete the proof of these conjectures.

Keywords

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