InformWrite the author - but not the way you've suggested!
It sounds like you've written him:
Hello Prof XYZ. I'm citing your work so now you owe me. Please do some free work for me! Figure out what I'm working on, see whether any of your work applies, and summarize your findings for me so I could publish more.
No no no no no, don't send that kind of a message.
I suggest that:
- You greet them
- You mention how them work on ABC has been inspirational for you, or how it attracted you to study ABC further etc.
- Tell them that you've been able to show whatever you've shown, and that X from their paper was key to achieving Y / helped lay the foundations for Z / gave you the idea to establish Y.
- If you want to ask him whether they explored a specific research direction X' following their work on X, ask.
- Don't ask them to do something for you. That might be relevant once you've established a rapport - and probably not even then. You can ask them for a suggestion regarding something to read; or for documents they have access to and you don't.