Positive limit-Fourier transform of Farey fractions

DOI10.1016/j.jnt.2014.10.003zbMath1369.11016arXiv1310.2709OpenAlexW2963076938MaRDI QIDQ2254221

Johannes Maria Singer

Publication date: 4 February 2015

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.2709

zbMATH Keywords

Fourier transformRiemann zeta function(modified) Farey fractions

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) Farey sequences; the sequences (1^k, 2^k, dots) (11B57) Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

Related Items (1)

Remark on the Farey fraction spin chain

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotics of the Farey fraction spin chain free energy at the critical point
• The number-theoretical spin chain and the Riemann zeroes
• On a ferromagnetic spin chain
• A Farey fraction spin chain
• The phase transition in statistical models defined on Farey fractions
• A fully magnetizing phase transition
• Generalized number theoretic spin chain-connections to dynamical systems and expectation values
• Thermodynamics of Farey fraction spin chain
• Cluster approximation for the Farey fraction spin chain
• A dichotomy between uniform distributions of the Stern-Brocot and the Farey sequence
• NUMBER THEORY, DYNAMICAL SYSTEMS AND STATISTICAL MECHANICS
• A POLYNOMIAL ANALOGUE TO THE STERN SEQUENCE
• Stern's Diatomic Sequence 0,1,1,2,1,3,2,3,1,4,…
• Gaussian correlation inequalities for ferromagnets
• Free energy and correlations of the number-theoretical spin chain
• The phase transition of the number-theoretical spin chain
• Products of matrices and and the distribution of reduced quadratic irrationals
• Zeros of the partition function for generalized ising systems
• The limit distribution of a number theoretic function arising from a problem in statistical mechanics
• On asymptotic properties of a number theoretic function arising out of a spin chain model in statistical mechanics

This page was built for publication: Positive limit-Fourier transform of Farey fractions