Is it appropriate to ask for an opinion about a preprint from researchers I don't personally know before submission? I'm writing a paper as a Ph.D. student, and I'm starting to feel a little bit unsure about the general approach and results. My supervisor isn't a great help here, and I thought to maybe send a preprint to a couple of authors with more expertise than me, whom I cited a lot, and ask their opinion and if they would find it of interest.
Is this appropriate? I wonder if it would look like I ask them to work as my reviewer or supervisor for free, or I would even look like one of these crazy persons sending researchers their huge manuscripts with fringe theories. On the other hand, I would get feedback during peer review anyway, so I'm further unsure about it.
In my field (mathematics) it is somewhat common to send out preprints like this, especially for junior researchers like yourself.
In my experience, the most common way is to send a copy of the paper as an attachment, briefly introduce yourself and the paper, and say something like &quot;I would welcome any comments if you have any. Thank you very much.&quot;
In particular I would not recommend asking questions, at least not in an initial email. I would especially avoid questions such as &quot;would you find this of interest&quot;, which can be very awkward to answer. As you said, you want to avoid looking like you're asking them to serve as a reviewer or supervisor.
That said, in my opinion, sending a paper and indicating that you'd welcome feedback is a perfectly fine thing to do. I've got some interesting feedback this way as a grad student, and more recently I've responded to similar emails coming from students.
Good luck!