I am in the process of making my first journal submission. Half-way through submission, I realise that I haven't considered the cover letter, which is an optional field in the submission process for this particular journal.
The history of my article is that the subject of the original paper is of tangential, but real, relevance to my PhD thesis. Having read the article, which is highly theoretical and technical and not in my area of expertise, I was pretty sure that I couldn't understand it properly—it seemed, if I followed it through correctly, to predict straightforwardly incorrect results. After struggling for several months in trying to get to grips with it, I swallowed my pride and reached out to a couple of the authors. It turned out that I wasn't misunderstanding after all, and the problems were real. They mentioned that if I could see a solution, they'd be happy to hear about it. I thought about it hard for a while and sent them my thoughts regarding a solution that they (people interested in this framework) might use, and they, surprisingly to me, suggested I submit them to the journal in question.
I should point out that these problems only affect a very narrow area of the ground covered in the the original paper, albeit an important one.
So my question is, given that this is a response to another article, firstly, do I need to give my article a 'sell' as it were, or can I just say that I am submitting it? Secondly, if I do write a more detailed letter, should I mention that (some of) the original authors suggested that I submit it, or that I have been in correspondence with them? Is it ok/wise to forego a cover letter completely?