Difference integrability conditions for parameterized linear difference and differential equations

[1]  Michio Jimbo,et al.  Deformation of linear ordinary differential equations, II , 1980 .

[2]  Michio Jimbo,et al.  Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. III , 1981 .

[3]  Michio Jimbo,et al.  Monodromy preserving deformation of linear ordinary differential equations with rational coefficients: I. General theory and τ-function , 1981 .

[4]  Yasutaka Sibuya,et al.  Linear Differential Equations in the Complex Domain: Problems of Analytic Continuation , 1990 .

[5]  Éric Schost,et al.  Linear Recurrences with Polynomial Coefficients and Computation of the Cartier-Manin Operator on Hyperelliptic Curves , 2003, International Conference on Finite Fields and Applications.

[6]  Claude Sabbah,et al.  The work of Andrey Bolibrukh on isomonodromic deformations , 2006 .

[7]  Alin Bostan,et al.  Low complexity algorithms for linear recurrences , 2006, ISSAC '06.

[8]  P. Gaudry,et al.  Linear Recurrences with Polynomial Coefficients and Application to Integer Factorization and Cartier-Manin Operator , 2007, SIAM J. Comput..

[9]  Charlotte Hardouin,et al.  Hypertranscendance des systèmes aux différences diagonaux , 2008, Compositio Mathematica.

[10]  Michael F. Singer,et al.  Differential Galois theory of linear difference equations , 2008, 0801.1493.

[11]  Sergei A. Abramov,et al.  Factorization of Polynomials and GCD Computations for Finding Universal Denominators , 2010, CASC.

[12]  Charlotte Hardouin,et al.  Courbures, groupes de Galois gnriques et D-groupode de Galois d'un systme aux q-diffrences , 2010 .

[13]  Sergei A. Abramov,et al.  Rational solutions of linear difference equations: Universal denominators and denominator bounds , 2011, Programming and Computer Software.

[14]  Nalini Joshi,et al.  Exact solutions of a q-discrete second Painlevé equation from its iso-monodromy deformation problem: I. Rational solutions , 2011, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[15]  Charlotte Hardouin,et al.  Descent for differential Galois theory of difference equations: confluence and q-dependence , 2011, 1103.5067.

[16]  Moulay A. Barkatou,et al.  Computing closed form solutions of integrable connections , 2012, ISSAC.

[17]  Lucia Di Vizio,et al.  Galois theories of q-difference equations: comparison theorems , 2012, Confluentes Mathematici.

[18]  Marius van der Put,et al.  Galois Theory of Linear Differential Equations , 2012 .

[19]  Lucia Di Vizio,et al.  Parameterized generic Galois groups for q-difference equations, followed by the appendix "The Galois D-groupoid of a q-difference system" by Anne Granier , 2012 .

[20]  Carlos E. Arreche.  Computing the differential Galois group of a one-parameter family of second order linear differential equations , 2012, 1208.2226.

[21]  Nalini Joshi,et al.  Exact solutions of a q-discrete second Painlevé equation from its iso-monodromy deformation problem. II. Hypergeometric solutions , 2012, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[22]  Alexey Ovchinnikov,et al.  Parameterized Picard-Vessiot extensions and Atiyah extensions , 2013 .

[23]  Michael Wibmer,et al.  Difference Galois theory of linear differential equations , 2013, 1302.7198.

[24]  Michael Wibmer,et al.  {\sigma}-Galois theory of linear difference equations , 2013, 1304.2649.

[25]  Alexey Ovchinnikov,et al.  Integrability conditions for parameterized linear difference equations , 2013, ISSAC '13.

[26]  Michael F. Singer,et al.  Unipotent differential algebraic groups as parameterized differential Galois groups , 2013, Journal of the Institute of Mathematics of Jussieu.

[27]  Thomas Dreyfus,et al.  Computing the Galois group of some parameterized linear differential equation of order two , 2011, 1110.1053.

[28]  Alexey Ovchinnikov,et al.  Isomonodromic differential equations and differential categories , 2012, 1202.0927.

[29]  Michael F. Singer,et al.  Reductive Linear Differential Algebraic Groups and the Galois Groups of Parameterized Linear Differential Equations , 2013, 1304.2693.