Cool stuff. I don't know enough about QFT to evaluate it, but involvment in basic physics of the zeta function to evaluate diverging series and so on is something really amazing. This video discusses L-functions and QFT:

https://www.youtube.com/watch?v=-OxVsVUesSc

About the Planck length, while the length itself might not be physically significant, black holes are definitely physically significant, and according to the current thinking there will be some smallest length that can be probed before what you're looking at becomes a black hole. I guess I was lazily assuming that would be around the Planck length. I would have to look into it more to come up with a calculation for that