Conjugation: Do we cite authors or papers? When referencing to another work in a scientific paper, do we cite the paper or its author(s)?

This question is intended to clarify the conjugation of the verb that follows the reference -- especially in these cases:


One author, two papers:


  Jane Doe (2015a, 2015b) list-s the very specific conditions under which...


-> lists (singular: referencing to Jane Doe) or list (plural: referencing to both papers)
Several authors, one paper:


  John Doe, et al. (2015) claim-s this and that.


-> claim (plural: referencing to the multiple authors of the paper) or claims (singular: referencing to the single paper).
I would say that it depends of the citation format, and the point is to look what is the subject of the sentence. In the examples you present, the conjugacy would be with the authors and the parenthesis only provides a precision about which paper is concerned. 

In math we usually cite like that:


  It is proved in [Doe15] that ...
  
  
  
  References
  
  [Doe15] Jane Doe, "paper name" Journal name, 2015


Therefore, we tend to cite the papers. However I often write


  In [Doe15], Jane Doe proves that...


where the conjugacy is obvious.