Over 25 years ago I wrote a paper with the pretentious title “Invariant distributions on the n-fold metaplectic covers of GL(r,F), F p-adic” (J. Fourier Anal. and Appl. 7(2001)343-358.). In fact, it was on such invariant distributions restricted to a very special class of functions where everything was much simpler to describe.

Inspired by a blog post of Professor Alonso Castillo-Ramirez, I asked AI to look over this paper. Here, by AI I mean using both chatGPT-Sol and claude-Fable or claude-Opus, teaming one up against the other (so they had to find my errors and, if any, also those of the other AI agent). Apparently, my “simple” argument was a bit confusing to the AI I used. This in turn confused me, until I started to remember the argument. Then I explained the argument to AI, and it got back on track. None-the-less, I’m happy for the diversion because it helped AI look into generalizations. Anything leading to more interesting mathematics is a positive thing, IMHO.

The long story short here is that I was sloppy with some definitions and some hypotheses, and I apologize for that. The usual excuse is that family and work obbligations are to blame but in fact, I love hunting down new and interesting mathematical arguments but I’m less enthusiastic about double-checking details. So, it’s really my fault. However, the overall results are more-or-less correct and even appear (if you believe AI) to generalize significantly. I have not pursued these generalizations. Nor will I, as I’ve been retired and out of that field for some time and no longer have access to the needed literature. For anyone interested, available are the original 2000 paper, the AI-aided corrected paper (2026), and AI-generated notes on generalizing these results are also available. Just email me.