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Quantum Graphs Whose Spectra Mimic the Zeros of the Riemann Zeta Function

URN to cite this document:
urn:nbn:de:bvb:355-epub-295725
Kuipers, Jack ; Hummel, Quirin ; Richter, Klaus
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arXiv PDF (26.02.2014)
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arXiv PDF (23.07.2013)
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Date of publication of this fulltext: 26 Feb 2014 08:21



Abstract

One of the most famous problems in mathematics is the Riemann hypothesis: that the nontrivial zeros of the Riemann zeta function lie on a line in the complex plane. One way to prove the hypothesis would be to identify the zeros as eigenvalues of a Hermitian operator, many of whose properties can be derived through the analogy to quantum chaos. Using this, we construct a set of quantum graphs that ...

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