Communications in Number Theory and Physics
Volume 5 (2011)
Abstract intersection theory and operators in Hilbert space
Pages: 699 – 712
For an operator in Hilbert space of a certain class, we introduce axioms of an abstract intersection theory, which we prove to be equivalent to the Riemann hypothesis regarding the spectrum of that operator. In particular, if the nontrivial zeros of the Riemann zeta-function arise from an operator of this class, the original Riemann hypothesis is equivalent to the existence of an abstract intersection theory.