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Quantum Graphs Whose Spectra Mimic the Zeros of the Riemann Zeta Function
Physical Review Letters
One of the most famous problems in mathematics is the Riemann hypothesis: that the non-trivial 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 have the same oscillating part of the density of states as the Riemann zeros, offering andoi:10.1103/physrevlett.112.070406 pmid:24579575 fatcat:tmftggxrsbhfvdaayjaxo32bxy