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

Kaya Lakein; Anne Larsen

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arXiv · 2107.07637

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

Kaya Lakein·Anne Larsen

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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.

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Kaya Lakein, Anne Larsen. 2021-07-15. A Proof of Merca's Conjectures on Sums of Odd Divisor Functions. https://arxiv.org/abs/2107.07637

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