Some investigations on the Riemann hypothesis with computers

The talk will survey some connections between RH and calculations on computers, abstract and electronic, in particular: Exact verification of RH for small zeroes on computers with limited precision; A connection between RH and the P = NP problem; Position of RH in the arithmetical hierachy and its heuristic significance; Proof of Turan's inequalities (a corollary to RH) by calculations.