9 citations · 12 across the 10 of their papers we have counts for
12 papers
A Tau function for -Painlevé VI as a Fredholm determinant
Harini Desiraju, Pieter Roffelsen
We give an analytic construction of a tau function for the -difference sixth Painlevé equation (PVI) as a Fredholm determinant through the general Riemann-Hilbert problem ass…
On difference-differential Lax pairs and integrals of Painlevé equations in finite characteristic
Nalini Joshi, Tomas Lasic Latimer, Pieter Roffelsen
We collect rank two difference-differential Lax pairs for classical Painlevé equations in the literature and put each in matrix form with the coefficient matrix of the…
On integrals of non-autonomous dynamical systems in finite characteristic
Nalini Joshi, Pieter Roffelsen
We use a difference Lax form to construct simultaneous integrals of motion of the fourth Painlevé equation and the difference second Painlevé equation over fields with finite chara…
Arithmetic dynamics of a discrete Painlevé equation
Nalini Joshi, Pieter Roffelsen
We consider the orbits of a discrete Painlevé equation over finite fields and show that the number of points in such orbits satisfy the Hasse bound. The orbits turn out to lie on a…
On the crystal limit of the q-difference sixth Painlevé equation
Nalini Joshi, Pieter Roffelsen
We consider the Riemann-Hilbert correspondence associated with the -difference sixth Painlevé equation in the crystal limit, i.e. , and show two main results. Fi…
Segre surfaces and geometry of the Painlevé equations
Nalini Joshi, Marta Mazzocco, Pieter Roffelsen
In this paper, we consider a six parameter family of affine Segre surfaces embedded in . For generic values of the parameters, this family is associated to the -dif…
On a class of elliptic orthogonal polynomials and their integrability
Harini Desiraju, Tomas Lasic Latimer, Pieter Roffelsen
Building upon the recent works of Bertola; Fasondini, Olver and Xu, we define a class of orthogonal polynomials on elliptic curves and establish a corresponding Riemann-Hilbert fra…
On -Painlevé VI and the geometry of Segre surfaces
Pieter Roffelsen
In the context of -Painlevé VI with generic parameter values, the Riemann-Hilbert correspondence induces a one-to-one mapping between solutions of the nonlinear equation and poi…
On symmetric solutions of the fourth -Painlevé equation
Nalini Joshi, Pieter Roffelsen
The Painlevé equations possess transcendental solutions with special initial values that are symmetric under rotation or reflection in the complex -plane. They correspond…
On the monodromy manifold of -Painlevé VI and its Riemann-Hilbert problem
Nalini Joshi, Pieter Roffelsen
We study the sixth -difference Painlevé equation () through its associated Riemann-Hilbert problem (RHP) and show that the RHP is always solvable fo…
On the Riemann-Hilbert problem for a -difference Painlevé equation
Nalini Joshi, Pieter Roffelsen
A Riemann-Hilbert problem for a -difference Painlevé equation, known as , is shown to be solvable. This yields a bijective correspondence between the…
Analytic solutions of - near its critical points
Nalini Joshi, Pieter Roffelsen
For transcendental functions that solve non-linear -difference equations, the best descriptions available are the ones obtained by expansion near critical points at the origin a…