The number-theoretical spin chain and the Riemann zeroes

DOI10.1007/s002200050441zbMath0926.11059OpenAlexW2048334225MaRDI QIDQ1290537

Andreas Knauf

Publication date: 2 December 1999

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s002200050441

zbMATH Keywords

zerosRiemann zeta-functionRiemann hypothesisferromagnetic propertyLewis equationnumber theoretical spin chainRamanujan characterspectral radii of Markov chains

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Miscellaneous applications of number theory (11Z05) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26)

Related Items (11)

Phase Operator on $$L^2(\mathbb {Q}_p)$$ and the Zeroes of Fisher and Riemann ⋮ On the convergence to equilibrium of unbounded observables under a family of intermittent interval maps ⋮ Müntz formula and zero free regions for the Riemann zeta function ⋮ A lattice gas of prime numbers and the Riemann hypothesis ⋮ Generalized Farey trees, transfer operators and phase transitions ⋮ Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions ⋮ Positive limit-Fourier transform of Farey fractions ⋮ Generalized number theoretic spin chain-connections to dynamical systems and expectation values ⋮ A thermodynamic classification of real numbers ⋮ Cluster approximation for the Farey fraction spin chain ⋮ NUMBER THEORY, DYNAMICAL SYSTEMS AND STATISTICAL MECHANICS

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