# Riemann Hypothesis and Complexity Theory

It is known that "Assuming the generalized Riemann hypothesis (GRH) if VP = VNP then PH collapses to second level". Why would one think of a relation between VP,VNP and the Riemann hypothesis. Where does a statement about the zeros of the Riemann zeta function appear in a statement about complexity classes ? I have not read the original result. It would be nice if anyone could provide some intuition.

• What rings is this statement about? Anyway, the VP and VNP classes are really more "algebraic geometry classes" than "computational complexity classes", so that's why. – Emil Jeřábek May 8 '17 at 8:20
• How many algebraic geometers can write down the proper definition of VNP ;-) – Markus Bläser May 8 '17 at 12:31