You can't do this with present version of eZ publish.
It may be possible to add code to count the views a particular element has received or count the number of times some piece of code that serves the pdf file has run.
However I think the best approach may be to look at your web server and find if there is something that can be done there. At the end of the day it is the server that delivers the file. Ez publish will in general just provide a link to it, which the web server has access to.
If you are using the content/download functionality then you could create your own binaryfile handler.
Take a look at <i>kernel/classes/binaryhandlers/ezfilepasstrough/ezfilepasstroughhandler.php</i> which is the default handler. Here you could check a custom database table based on the user ID to figure out how many times it has been downloaded.
Ofcourse this requires that you know how to program PHP.
