scholarly journals Perturbations of the Spence–Abel equation and deformations of the dilogarithm function

2017 ◽  
Vol 368 (3-4) ◽  
pp. 1399-1428 ◽  
Author(s):  
Tobias Hartnick ◽  
Andreas Ott
Keyword(s):  
Abel Equation ◽  
Dilogarithm Function

scholarly journals Quantum periods and TBA-like equations for a class of Calabi-Yau geometries

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bao-ning Du ◽  
Min-xin Huang
Keyword(s):  
Large Class ◽  
Bethe Ansatz ◽  
Difference Equations ◽  
The Other ◽  
Elementary Functions ◽  
Quantum Dilogarithm ◽  
Thermodynamic Bethe Ansatz ◽  
Dilogarithm Function ◽  
Quantum Operators

Abstract We continue the study of a novel relation between quantum periods and TBA(Thermodynamic Bethe Ansatz)-like difference equations, generalize previous works to a large class of Calabi-Yau geometries described by three-term quantum operators. We give two methods to derive the TBA-like equations. One method uses only elementary functions while the other method uses Faddeev’s quantum dilogarithm function. The two approaches provide different realizations of TBA-like equations which are nevertheless related to the same quantum period.

scholarly journals Functional equations of iterated integrals with regular singularities

1996 ◽  
Vol 142 ◽  
pp. 145-159 ◽  
Author(s):  
Zdzisław Wojtkowiak
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
The Other ◽  
Abel Equation ◽  
Iterated Integrals

Polylogarithmic functions satisfy functional equations. The most famous equation is of course the functional equation of the logarithmlog x + log y = log(x · y).The other well known equation is the Abel equation of the dilogarithm

Stewart-Lyth second-order approach as an Abel equation for reconstructing inflationary dynamics

1997 ◽  
Vol 229 (1) ◽  
pp. 32-36 ◽  
Author(s):  
Alberto García ◽  
Alfredo Macías ◽  
Eckehard W. Mielke
Keyword(s):  
Second Order ◽  
Abel Equation

scholarly journals Green's function for the Laplace–Beltrami operator on a toroidal surface

2013 ◽  
Vol 469 (2149) ◽  
pp. 20120479 ◽  
Author(s):  
Christopher C. Green ◽  
Jonathan S. Marshall
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Vortex Dynamics ◽  
Stereographic Projection ◽  
Three Dimensional ◽  
Beltrami Operator ◽  
Toroidal Surface ◽  
Torus Surface ◽  
Dilogarithm Function ◽  
Prime Function

Green's function for the Laplace–Beltrami operator on the surface of a three-dimensional ring torus is constructed. An integral ingredient of our approach is the stereographic projection of the torus surface onto a planar annulus. Our representation for Green's function is written in terms of the Schottky–Klein prime function associated with the annulus and the dilogarithm function. We also consider an application of our results to vortex dynamics on the surface of a torus.

scholarly journals FRACTAL INDEX, CENTRAL CHARGE AND FRACTONS

2000 ◽  
Vol 15 (31) ◽  
pp. 1931-1939 ◽  
Author(s):  
WELLINGTON DA CRUZ ◽  
ROSEVALDO DE OLIVEIRA
Keyword(s):  
Hausdorff Dimension ◽  
Central Charge ◽  
Statistical Parameter ◽  
Conformal Anomaly ◽  
Fermi Velocity ◽  
Conformal Field ◽  
Fractal Index ◽  
Fractal Statistics ◽  
Universal Classes ◽  
Dilogarithm Function

We introduce the notion of fractal index associated with the universal class h of particles or quasiparticles, termed fractons which obey specific fractal statistics. A connection between fractons and conformal field theory (CFT)-quasiparticles is established taking into account the central charge c[ν] and the particle-hole duality ν↔1/ν, for integer-value ν of the statistical parameter. In this way, we derive the Fermi velocity in terms of the central charge as [Formula: see text]. The Hausdorff dimension h which labeled the universal classes of particles and the conformal anomaly are therefore related. Following another route, we also established a connection between Rogers dilogarithm function, Farey series of rational numbers and the Hausdorff dimension.

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