Abstract intersection theory and operators in Hilbert space

Details Abstract intersection theory and operators in Hilbert space Abstract intersection theory and operators in Hilbert space

2009-08-20

arxiv.org/abs/0908.2909v1

Mathematics

Number Theory

Scientific paper

For an operator of a certain class in Hilbert space, we introduce axioms of an abstract intersection theory, which we prove to be equivalent to the Riemann Hypothesis concerning 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.

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