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math-ph2025
Modular transformations of tau functions and conformal blocks on the torus
Fabrizio Del Monte, Harini Desiraju, Pavlo Gavrylenko
The connection problem for isomonodromic tau functions on the one-punctured torus concerns the ratio between the tau function and its modular transform, associated to dual pants de…
math-ph2025
Riemann-Hilbert problems, Fredholm determinants, explicit combinatorial expansions, and connection formulas for the general -Painlevé III tau functions
Pavlo Gavrylenko
We reformulate the -difference linear system corresponding to the -Painlevé equation of type as a Riemann-Hilbert problem on a circle. Then, we consider the Fre…