unfortunately everyone is now doing this with LLMs, it actually feels like it might be on its way to being a negative signal, as strange as that sounds.
What always worked for me is something like, "Hey, I read your book!" or "I just heard your interview on the radio!"
It's especially effective if it's a timely event. People do talks and interviews to meet people and get some attention, so you're basically shaking hands with someone who's ready to shake yours.
Yes, this is dangerous because the author is an expert who will know bullshit when they read it.
On the other hand, at least make sure you have looked into what the LLM says about your questions. It is aggravating to get a request which an LLM can answer correctly.
It's especially effective if it's a timely event. People do talks and interviews to meet people and get some attention, so you're basically shaking hands with someone who's ready to shake yours.