Michael F. Singer

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All published works

Action	Title	Year	Authors
+	Telescopers for differential forms with one parameter	2024	Shaoshi Chen Ruyong Feng Ziming Li Michael F. Singer Stephen M. Watt
+ PDF Chat	On the algebraic dependence of holonomic functions	2022	Julien Roques Michael F. Singer
+	Comments on Rosenlicht’s Integration in Finite Terms	2022	Michael F. Singer
+ PDF Chat	On differentially algebraic generating series for walks in the quarter plane	2021	Charlotte Hardouin Michael F. Singer
+ PDF Chat	Sparse Interpolation in Terms of Multivariate Chebyshev Polynomials	2021	Évelyne Hubert Michael F. Singer
+	Separability Problems in Creative Telescoping	2021	Shaoshi Chen Ruyong Feng Pingchuan Ma Michael F. Singer
+	Separability Problems in Creative Telescoping	2021	Shaoshi Chen Ruyong Feng Pingchuan Ma Michael F. Singer
+ PDF Chat	On the Kernel Curves Associated with Walks in the Quarter Plane	2021	Thomas Dreyfus Charlotte Hardouin Julien Roques Michael F. Singer
+	Telescopers for differential forms with one parameter	2021	Shaoshi Chen Ruyong Feng Ziming Li Michael F. Singer Stephen M. Watt
+ PDF Chat	Local rigidity of Einstein 4-manifolds satisfying a chiral curvature condition	2020	Joël Fine Kirill Krasnov Michael F. Singer
+	On Differentially Algebraic Generating Series for Walks in the Quarter Plane	2020	Charlotte Hardouin Michael F. Singer
+	On the Kernel curves associated with walks in the quarter plane	2020	Thomas Dreyfus Charlotte Hardouin Julien Roques Michael F. Singer
+	Walks in the quarter plane: Genus zero case	2020	Thomas Dreyfus Charlotte Hardouin Julien Roques Michael F. Singer
+	On the Kernel curves associated with walks in the quarter plane	2020	Thomas Dreyfus Charlotte Hardouin Julien Roques Michael F. Singer
+	On Differentially Algebraic Generating Series for Walks in the Quarter Plane	2020	Charlotte Hardouin Michael F. Singer
+ PDF Chat	Consistent systems of linear differential and difference equations	2019	Reinhard Schäfke Michael F. Singer
+ PDF Chat	Walks in the quarter plane, genus zero case	2018	Thomas Dreyfus Charlotte Hardouin Julien Roques Michael F. Singer
+ PDF Chat	On the nature of the generating series of walks in the quarter plane	2018	Thomas Dreyfus Charlotte Hardouin Julien Roques Michael F. Singer
+ PDF Chat	Galois groups for integrable and projectively integrable linear difference equations	2017	Carlos E. Arreche Michael F. Singer
+ PDF Chat	THE SPACE OF HYPERKÄHLER METRICS ON A 4-MANIFOLD WITH BOUNDARY	2017	Joël Fine Jason D. Lotay Michael F. Singer
+ PDF Chat	Asymptotics of Partial Density Functions for Divisors	2016	Julius Ross Michael F. Singer
+	Mahler equations and rationality	2016	Reinhard Schäfke Michael F. Singer
+	Desingularization of Ore operators	2015	Shaoshi Chen Manuel Kauers Michael F. Singer
+ PDF Chat	Parallel telescoping and parameterized Picard-Vessiot theory	2014	Shaoshi Chen Ruyong Feng Ziming Li Michael F. Singer
+	On the summability of bivariate rational functions	2014	Shaoshi Chen Michael F. Singer
+ PDF Chat	Reductive Linear Differential Algebraic Groups and the Galois Groups of Parameterized Linear Differential Equations	2014	Andrey Minchenko Alexey Ovchinnikov Michael F. Singer
+	Desingularization of Ore Operators	2014	Shaoshi Chen Manuel Kauers Michael F. Singer
+	Parallel Telescoping and Parameterized Picard--Vessiot Theory	2014	Shaoshi Chen Ruyong Feng Ziming Li Michael F. Singer
+ PDF Chat	Toric partial density functions and stability of toric varieties	2013	Florian T. Pokorny Michael F. Singer
+ PDF Chat	Unipotent differential algebraic groups as parameterized differential Galois groups	2013	Andrey Minchenko Alexey Ovchinnikov Michael F. Singer
+ PDF Chat	Desingularization explains order-degree curves for ore operators	2013	Shaoshi Chen Maximilian Jaroschek Manuel Kauers Michael F. Singer
+	Unipotent dierential algebraic groups as parameterized dierential Galois groups	2013	Andrey Minchenko Alexey Ovchinnikov Michael F. Singer
+	Desingularization Explains Order-Degree Curves for Ore Operators	2013	Shaoshi Chen Maximilian Jaroschek Manuel Kauers Michael F. Singer
+	Linear algebraic groups as parameterized Picard–Vessiot Galois groups	2012	Michael F. Singer
+ PDF Chat	Telescopers for rational and algebraic functions via residues	2012	Shaoshi Chen Manuel Kauers Michael F. Singer
+	Residues and telescopers for bivariate rational functions	2012	Shaoshi Chen Michael F. Singer
+ PDF Chat	Monodromy groups of parameterized linear differential equations with regular singularities	2012	Claude Mitschi Michael F. Singer
+	Residues and Telescopers for Rational Functions	2012	Shaoshi Chen Michael F. Singer
+	Telescopers for Rational and Algebraic Functions via Residues	2012	Shaoshi Chen Manuel Kauers Michael F. Singer
+	On the Summability of Bivariate Rational Functions	2012	Shaoshi Chen Michael F. Singer
+	Toric partial density functions and stability of toric varieties	2011	Florian T. Pokorny Michael F. Singer
+	Toric Slope Stability and Partial Bergman Kernels	2011	Florian T. Pokorny Michael F. Singer
+	Linear Algebraic Groups as Parameterized Picard-Vessiot Galois Groups	2011	Michael F. Singer
+	Linear Algebraic Groups as Parameterized Picard-Vessiot Galois Groups	2011	Michael F. Singer
+ PDF Chat	A Jordan–Hölder Theorem for differential algebraic groups	2010	Phyllis J. Cassidy Michael F. Singer
+ PDF Chat	Projective Isomonodromy and Galois Groups	2010	Claude Mitschi Michael F. Singer
+	A Jordan-Hoelder Theorem for Differential Algebraic Groups	2010	Phyllis J. Cassidy Michael F. Singer
+	Projective Isomonodromy and Galois Groups	2010	Claude Mitschi Michael F. Singer
+	An algorithm to compute Liouvillian solutions of prime order linear difference–differential equations	2009	Ruyong Feng Michael F. Singer Min Wu
+	Liouvillian solutions of linear difference–differential equations	2009	Ruyong Feng Michael F. Singer Min Wu
+ PDF Chat	Galois Theory of Linear Differential Equations	2008	Michael F. Singer
+ PDF Chat	Differential Galois theory of linear difference equations	2008	Charlotte Hardouin Michael F. Singer
+ PDF Chat	On the definitions of difference Galois groups	2008	Zoé Chatzidakis Charlotte Hardouin Michael F. Singer
+	Liouvillian Solutions of Difference-Differential Equations	2008	Ruyong Feng Michael F. Singer Min Wu
+	Differential Galois Theory of Linear Difference Equations	2008	Charlotte Hardouin Michael F. Singer
+ PDF Chat	Model Theory with Applications to Algebra and Analysis: On the definitions of difference Galois groups	2008	Zoé Chatzidakis Charlotte Hardouin Michael F. Singer
+ PDF Chat	Model theory of partial differential fields: From commuting to noncommuting derivations	2007	Michael F. Singer
+	Introduction to the Galois Theory of Linear Differential Equations	2007	Michael F. Singer
+	On the Definitions of Difference Galois Groups	2007	Zoé Chatzidakis Charlotte Hardouin Michael F. Singer
+ PDF Chat	Galois theory of parameterized differential equations and linear differential algebraic groups	2006	Phyllis J. Cassidy Michael F. Singer
+ PDF Chat	A recursive method for determining the one-dimensional submodules of Laurent-Ore modules	2006	Ziming Li Michael F. Singer Min Wu Dabin Zheng
+	A Recursive Method for Determining the One-Dimensional Submodules of Laurent-Ore Modules	2006	Ziming Li Michael F. Singer Min Wu Dabin Zheng
+	Model Theory of Partial Differential Fields: From Commuting to Noncommuting Derivations	2006	Michael F. Singer
+ PDF Chat	On the Constructive Inverse Problem in Differential Galois Theory#	2005	William J. Cook Claude Mitschi Michael F. Singer
+	Galois Theory of Parameterized Differential Equations and Linear Differential Algebraic Groups	2005	Phyllis J. Cassidy Michael F. Singer
+	Galois Theory of Parameterized Dierential Equations	2005	Phyllis J. Cassidy Michael F. Singer
+	On the Constructive Inverse Problem in Differential Galois Theory	2004	William J. Cook Claude Mitschi Michael F. Singer
+	Stokes Matrices and Meromorphic Classification	2003	Marius van der Put Michael F. Singer
+	Picard-Vessiot Theory	2003	Marius van der Put Michael F. Singer
+	Monodromy, the Riemann-Hilbert Problem, and the Differential Galois Group	2003	Marius van der Put Michael F. Singer
+	Differential Operators and Differential Modules	2003	Marius van der Put Michael F. Singer
+	Differential Equations on the Complex Sphere and the Riemann-Hilbert Problem	2003	Marius van der Put Michael F. Singer
+	Universal Picard-Vessiot Rings and Galois Groups	2003	Marius van der Put Michael F. Singer
+	Inverse Problems	2003	Marius van der Put Michael F. Singer
+	Moduli for Singular Differential Equations	2003	Marius van der Put Michael F. Singer
+	Linear Differential Operators for Polynomial Equations	2002	Olivier Cormier Michael F. Singer Barry Trager Félix Ulmer
+ PDF Chat	Solvable-by-finite groups as differential Galois groups	2002	Claude Mitschi Michael F. Singer
+	Effective methods in algebraic geometry	2001	Michael F. Singer
+	Computing the Galois group of a polynomial using linear differential equations	2000	Olivier Cormier Michael F. Singer Félix Ulmer
+	Computing Galois Groups of Completely Reducible Differential Equations	1999	Élie Compoint Michael F. Singer
+	Calculating the Galois group of L1(L2(y))=0,L1,L2 completely reducible operators	1999	Peter Berman Michael F. Singer
+	Solving Difference Equations in Finite Terms	1999	P.A. Hendricks Michael F. Singer
+	Linear differential equations and products of linear forms	1997	Michael F. Singer Félix Ulmer
+	Picard-Vessiot rings	1997	Marius van der Put Michael F. Singer
+	Difference modules over $$\mathcal{P}$$	1997	Marius van der Put Michael F. Singer
+	The inverse problem for difference equations	1997	Marius van der Put Michael F. Singer
+	Semi-regular difference equations	1997	Marius van der Put Michael F. Singer
+	Computing galois groups of linear differential equations of order four	1997	Sabrina Anne Hessinger Michael F. Singer
+ PDF Chat	Galois Theory of Difference Equations	1997	Marius van der Put Michael F. Singer
+	Connected Linear Groups as Differential Galois Groups	1996	Claude Mitschi Michael F. Singer
+ PDF Chat	On Ramis's solution of the local inverse problem of differential Galois theory	1996	Claude Mitschi Michael F. Singer
+ PDF Chat	On Magid's approach to the inverse problem in differential Galois theory.	1996	Jerry Kovacic Claude Mitschi Michael F. Singer
+	Testing reducibility of linear differential operators: A group theoretic perspective	1996	Michael F. Singer
+	Testing Reducibility of Linear Differential Operators: A Group Theoretic Perspective	1996	Michael F. Singer
+ PDF Chat	Connected Linear Groups as Differential Galois Groups over $C(x)$.	1995	Claude Mitschi Michael F. Singer
+	Group-theoretic obstructions to integrability	1995	Richard C. Churchill David L. Rod Michael F. Singer
+	On the integer zeros of exponential polynomials	1993	C. WardHenson Lee A. Rubel Lou van den Dries Michael F. Singer
+	Liouvillian and Algebraic Solutions of Second and Third Order Linear Differential Equations	1993	Michael F. Singer Félix Ulmer
+ PDF Chat	Liouvillian First Integrals of Differential Equations	1992	Michael F. Singer
+	Liouvillian solutions of third order linear differential equations	1992	Michael F. Singer Félix Ulmer
+ PDF Chat	Liouvillian first integrals of differential equations	1992	Michael F. Singer
+	Solving Ordinary Differential Equations in Terms of Series with Real Exponents	1991	Dima Grigoriev Michael F. Singer
+ PDF Chat	The interpolation problem for k-sparse sums of eigenfunctions of operators	1991	Dima Grigoriev Marek Karpiński Michael F. Singer
+	Liouvillian Solutions of Linear Differential Equations with Liouvillian Coefficients	1991	Michael F. Singer
+	Formal solutions of differential equations	1990	Michael F. Singer
+	Algebraic properties of the ring of general exponential polynomials	1989	C. Ward Henson Lee A. Rubel Michael F. Singer
+	Liouvillian first integrals of differential equations	1989	Michael F. Singer
+	Liouvillian Solutions of Linear Differential Equations with Liouvillian Coefficients	1989	Michael F. Singer
+	LIOUVILLIAN SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS WITH LIOUVILLIAN COEFFICmNTS Extended Abstract	1989	Michael F. Singer
+	Autonomous functions	1988	Lee A. Rubel Michael F. Singer
+	Algebraic Relations Among Solutions of Linear Differential Equations: Fano's Theorem	1988	Michael F. Singer
+	Elementary and Liouvillian Solutions of Linear Differential Equations	1986	James H. Davenport Michael F. Singer
+ PDF Chat	Algebraic Relations Among Solutions of Linear Differential Equations	1986	Michael F. Singer
+ PDF Chat	Algebraic relations among solutions of linear differential equations	1986	Michael F. Singer
+	A Classification of Differential Equations of Fuchsian Class	1985	Michael F. Singer Marvin Tretkoff
+	Some Applications of Linear Groups to Differential Equations	1985	Michael F. Singer Marvin Tretkoff
+	Solving Homogeneous Linear Differential Equations in Terms of Second Order Linear Differential Equations	1985	Michael F. Singer
+	A class of vectorfields on S2 that are topologically equivalent to polynomial vectorfields	1985	Stephen Schecter Michael F. Singer
+	Elementary and Liouvillian solutions of linear differential equations	1985	Michael F. Singer James H. Davenport
+ PDF Chat	A differentially algebraic elimination theorem with application to analog computability in the calculus of variations	1985	Lee A. Rubel Michael F. Singer
+ PDF Chat	Elementary First Integrals of Differential Equations	1983	M. J. Prelle Michael F. Singer
+ PDF Chat	Elementary first integrals of differential equations	1983	M. J. Prelle Michael F. Singer
+ PDF Chat	Erratum to: Separatrices at singular points of planar vector fields	1983	Stephen Schecter Michael F. Singer
+	Addendum to "Planar Polynomial Foliations"	1981	Stephen Schecter Michael F. Singer
+	Liouvillian Solutions of n-th Order Homogeneous Linear Differential Equations	1981	Michael F. Singer
+ PDF Chat	Addendum to: “Planar polynomial foliations”	1981	Stephen Schecter Michael F. Singer
+	Elementary first integrals of differential equations	1981	M. J. Prelle Michael F. Singer
+ PDF Chat	Planar Polynomial Foliations	1980	Stephen Schecter Michael F. Singer
+	Singular points of planar vector fields	1980	Stephen Schecter Michael F. Singer
+ PDF Chat	Separatrices at singular points of planar vector fields	1980	Stephen Schecter Michael F. Singer
+ PDF Chat	Planar polynomial foliations	1980	Stephen Schecter Michael F. Singer
+	Remarks on Analytic Continuation	1980	Franklin Haimo Michael F. Singer Marvin Tretkoff
+ PDF Chat	A Class of Differential Fields with Minimal Differential Closures	1978	Michael F. Singer
+	The model theory of ordered differential fields	1978	Michael F. Singer
+ PDF Chat	A class of differential fields with minimal differential closures	1978	Michael F. Singer
+ PDF Chat	Functions Satisfying Elementary Relations	1977	Michael F. Singer
+	On elementary, generalized elementary, and liouvillian extension fields	1977	Maxwell Rosenlicht Michael F. Singer
+ PDF Chat	Functions satisfying elementary relations	1977	Michael F. Singer
+ PDF Chat	Solutions of linear differential equations in function fields of one variable	1976	Michael F. Singer
+ PDF Chat	Elementary solutions of differential equations	1975	Michael F. Singer

Common Coauthors

Coauthor	Papers Together
Shaoshi Chen	16
Charlotte Hardouin	14
Marius van der Put	13
Claude Mitschi	10
Ruyong Feng	9
Stephen Schecter	8
Julien Roques	7
Manuel Kauers	6
Thomas Dreyfus	6
Ziming Li	6
Phyllis J. Cassidy	5
Félix Ulmer	5
Lee A. Rubel	4
Alexey Ovchinnikov	3
Min Wu	3
Florian T. Pokorny	3
Marvin Tretkoff	3
Andrey Minchenko	3
Zoé Chatzidakis	3
Reinhard Schäfke	2
Dabin Zheng	2
Olivier Cormier	2
Stephen M. Watt	2
Min Wu	2
Pingchuan Ma	2
Dima Grigoriev	2
Maximilian Jaroschek	2
James H. Davenport	2
William J. Cook	2
M. J. Prelle	2
Joël Fine	2
Julius Ross	1
Peter Berman	1
M. J. Prelle	1
Barry Trager	1
C. WardHenson	1
Sabrina Anne Hessinger	1
Jason D. Lotay	1
David L. Rod	1
Franklin Haimo	1
P.A. Hendricks	1
Carlos E. Arreche	1
Maxwell Rosenlicht	1
Évelyne Hubert	1
Élie Compoint	1
Jerry Kovacic	1
Kirill Krasnov	1
Lou van den Dries	1
C. Ward Henson	1
Marek Karpiński	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Differential Algebra and Algebraic Groups	2012	E. R. Kolchin	31
+	An introduction to differential algebra	1957	Irving Kaplansky	22
+ PDF Chat	On Liouville’s theory of elementary functions	1976	Maxwell Rosenlicht	17
+	Linear Algebraic Groups	1975	James E. Humphreys	16
+	Liouvillian Solutions of n-th Order Homogeneous Linear Differential Equations	1981	Michael F. Singer	14
+	Differential Algebraic Groups	1972	P. J. Cassidy	13
+	Solution of the Inverse Problem of Differential Galois Theory in the Classical Case	1979	Carol Tretkoff Marvin Tretkoff	13
+ PDF Chat	The problem of integration in finite terms	1969	Robert H. Risch	12
+	An algorithm for solving second order linear homogeneous differential equations	1986	J. Kovacic	12
+ PDF Chat	Differential Galois theory of linear difference equations	2008	Charlotte Hardouin Michael F. Singer	12
+	Introduction to the theory of linear differential equations	1936	Edgar Girard Croker Poole	12
+	Introduction to the Theory of Algebraic Functions of One Variable	1951	Claude Chevalley	10
+ PDF Chat	Galois Theory of Difference Equations	1997	Marius van der Put Michael F. Singer	9
+	An algorithmic proof theory for hypergeometric (ordinary and “q”) multisum/integral identities	1992	Herbert S. Wilf Doron Zeilberger	9
+ PDF Chat	Elementary solutions of differential equations	1975	Michael F. Singer	8
+	The classification of the semisimple differential algebraic groups and the linear semisimple differential algebraic Lie algebras	1989	Phyllis J. Cassidy	8
+	Finite singularities and hypergeometric solutions of linear recurrence equations	1999	Mark van Hoeij	8
+	Residues and telescopers for bivariate rational functions	2012	Shaoshi Chen Michael F. Singer	8
+	On the explicit solvability of certain transcendental equations	1969	Maxwell Rosenlicht	7
+	Basic Theory of Algebraic Groups and Lie Algebras	1981	G. Hochschild	7
+ PDF Chat	Monodromy groups of parameterized linear differential equations with regular singularities	2012	Claude Mitschi Michael F. Singer	7
+	Parameterized Picard–Vessiot extensions and Atiyah extensions	2013	Henri Gillet Sergey Gorchinskiy Alexey Ovchinnikov	7
+	Differential algebraic groups	1986	E. R. Kolchin	7
+ PDF Chat	Complexity of creative telescoping for bivariate rational functions	2010	Alin Bostan Shaoshi Chen Frédéric Chyzak Ziming Li	7
+ PDF Chat	Moduli of linear differential equations on the Riemann sphere with fixed Galois groups	1993	Michael Singer	7
+	Computing the Galois group of a linear differential equation	2002	Ehud Hrushovski	7
+	The method of differentiating under the integral sign	1990	Gert Almkvist Doron Zeilberger	7
+	Elementary and Liouvillian Solutions of Linear Differential Equations	1986	James H. Davenport Michael F. Singer	7
+	An introduction to pseudo-linear algebra	1996	Manuel Bronstein Marko Petkovšek	7
+	Testing reducibility of linear differential operators: A group theoretic perspective	1996	Michael F. Singer	7
+	On solutions of linear functional systems and factorization of modules over Laurent-Ore algebras	2005	Min Wu	7
+ PDF Chat	Differential extension fields of exponential type	1975	Maxwell Rosenlicht	6
+ PDF Chat	On the functions counting walks with small steps in the quarter plane	2012	Irina Kurkova Kilian Raschel	6
+	Complexity of irreducibility testing for a system of linear ordinary differential equations	1990	Dima Yu. Grigoriev	6
+	Galois Theory of Parameterized Differential Equations and Linear Differential Algebraic Groups	2005	Phyllis J. Cassidy Michael F. Singer	6
+ PDF Chat	Generalized differential Galois theory	2008	Peter Landesman	6
+ PDF Chat	Two non-holonomic lattice walks in the quarter plane	2009	Marni Mishna Andrew Rechnitzer	6
+	Greatest Factorial Factorization and Symbolic Summation	1995	Peter Paule	6
+	Constrained extensions of differential fields	1974	E. R. Kolchin	6
+ PDF Chat	Counting quadrant walks via Tutte's invariant method	2021	Olivier Bernardi Mireille Bousquet‐Mélou Kilian Raschel	6
+ PDF Chat	Tannakian Approach to Linear Differential Algebraic Groups	2008	Alexey Ovchinnikov	6
+	Liouvillian Solutions of Linear Differential Equations with Liouvillian Coefficients	1991	Michael F. Singer	6
+	Non-D-finite excursions in the quarter plane	2013	Alin Bostan Kilian Raschel Bruno Salvy	6
+	Linear algebraic groups	1966	Armand Borel	6
+	Linear algebraic groups as parameterized Picard–Vessiot Galois groups	2012	Michael F. Singer	6
+	Solving Homogeneous Linear Differential Equations in Terms of Second Order Linear Differential Equations	1985	Michael F. Singer	6
+	Existence of $\partial$-parameterized Picard-Vessiot extensions over fields with algebraically closed constants	2011	Michael Wibmer	6
+	A holonomic systems approach to special functions identities	1990	Doron Zeilberger	6
+ PDF Chat	The complete generating function for Gessel walks is algebraic	2010	Alin Bostan Manuel Kauers	6
+ PDF Chat	Abstract differential algebra and the analytic case	1958	A. Seidenberg	6