What papers can you ask someone to cite for using your software? Ofen Software authors request that users cite a paper of theirs in publications resulting from projects using their software.

As such an software author, what logic governs what kind of papers you can reasonably ask to cite?
I see 5 cases:


The paper is about the software explicitly. Eg Theano
The software is a direct implementation of an algorithm described in the paper. Eg anything from here
They created the software to use in research presented in the paper. It has not changed since.
They originally created the software for use in the research paper, but since then it has undergone fairly large changes as it has continued to be developed.  Eg DeepLearnToolbox
The paper has nothing in common with the software, except sharing an author. 


In which cases is it acceptable to request the paper be cited?
5 seems like an obvious no-no, but are the others in the clear?

This question is the flip-side of Should I cite Papers to acknowledge usage of tools?
When I am using someone else's software and this software has been used in my paper, the least I can do is cite the related paper. In many cases when the tool is available online, authors typically include the citation along with the download (on the readMe or documentation file). In those kind of cases, I must admit I have never really checked the overlap between the paper and the software, because citing the author's paper seemed to me more a matter of professional courtesy and attribution of their contribution to my work than anything else. After all, if I trust the authors enough to assume their software gives correct results, not trusting them for which paper they tell me to cite seemed like an oxymoron.

On the other hand, if I was the software author I would be careful so that there is a significant overlap between the paper and the software (your cases 1-4). All of those cases seem to me like a reasonable reason to cite the related paper. There is also a case 6 when the tool was developed during the duration of a research project and there is a published paper that describes this project. In that case, citing this paper like this: 


  We use the 'tool' that was developed during the 'myName' project
  [citationToMyNamePaper]"


when using this tool, would also seem like a reasonable choice.   

I must say that I have never met your case 5 ("The paper has nothing in common with the software"), when I actually checked for overlap. Do you have any concrete examples of such a case yourself? Because although something like that is possible, I do not think it is common.