Communications in Number Theory and Physics

Volume 5 (2011)

Number 3

Abstract intersection theory and operators in Hilbert space

Pages: 699 – 712

DOI: http://dx.doi.org/10.4310/CNTP.2011.v5.n3.a4

Authors

Grzegorz Banaszak (Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland)

Yoichi Uetake (Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland)

Abstract

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.

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