Riemann zeros and phase transitions via the spectral operator on fractal strings

DOI10.1088/1751-8113/45/37/374005zbMath1252.81067arXiv1203.4828OpenAlexW3104926476MaRDI QIDQ2920313

Michel L. Lapidus, Hafedh Herichi

Publication date: 16 October 2012

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.4828

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Spectrum, resolvent (47A10) General spectral theory of ordinary differential operators (34L05) Linear symmetric and selfadjoint operators (unbounded) (47B25) Groups and semigroups of linear operators (47D03) Research exposition (monographs, survey articles) pertaining to quantum theory (81-02) Inverse scattering problems in quantum theory (81U40) Symmetry breaking in quantum theory (81R40) Critical phenomena in equilibrium statistical mechanics (82B27) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Other Dirichlet series and zeta functions (11M41) Length, area, volume, other geometric measure theory (28A75) Fractals (28A80) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Linear accretive operators, dissipative operators, etc. (47B44) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35) Relations with noncommutative geometry (11M55)

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