I just thought about the critical concepts in mathematics and physics that arose in the last century: Goedel, Schroedinger, etc. My question is: Are there any physical theories that rely on the validity of the extended Riemann Hypothesis? I don't mean computer science, i.e. secure communications or encryption; pure physics. As modern physics depend more and more on some very abstract concepts, e.g. Kähler manifolds, de Sitter spaces and so on I asked myself whether the ERH slipped in somewhere.