A recent press release from the Viterbi School of Engineering at USC discussed the proof of the Lindelöf hypothesis by Athanassios Fokas, a visiting professor from the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge.
In the press release, it is noted that the proof has implications for computational complexity theory and quantum computing, but no real details are provided. I've skimmed the paper on arXiv.org, but I don't believe such implications are noted and (unfortunately) mathematical proofs are not my area of expertise.
So, as stated, my question is: How would a proof of the Lindelöf hypothesis improve our understanding of computational complexity classes? I'm especially interested in any refinements that relate to quantum computing (assuming they do in fact exist).