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Lauren Ipsum gives a good answer. I'll guess at the purpose of your query and suggest a message along these lines: Dear Dr. X, I recently read your paper, Y, and I was very interested in t...
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#3: Attribution notice added
Source: https://writers.stackexchange.com/a/6415 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
Lauren Ipsum gives a good answer. I'll guess at the purpose of your query and suggest a message along these lines: > Dear Dr. X, > > I recently read your paper, Y, and I was very interested in the proofs you sketched. My research is in a related area: (here you describe your research). > > Would it be possible for you to send me the complete proofs of the theorems? I would use these proofs to... (here you describe what you'd do). That is, Dr. X might be planning to do exactly what you'd like to do, so it would be useful to let him or her know what that is. You might suggest that the two of you could collaborate, but that depends to some extent on your current track record (i.e., it would be more attractive for Dr. X if your past work indicates that it would be a fruitful collaboration).