Michael F. Singer

Integration in Finite Terms: Fundamental Sources

On differentially algebraic generating series for walks in the quarter plane

SELECTA MATHEMATICA-NEW SERIES, 27(5).

On the Kernel Curves Associated with Walks in the Quarter Plane

TRANSCENDENCE IN ALGEBRA, COMBINATORICS, GEOMETRY AND NUMBER THEORY, TRANS19, Vol. 373, pp. 61–89.

Sparse Interpolation in Terms of Multivariate Chebyshev Polynomials

Hubert, E., & Singer, M. F. (2021, September 9). FOUNDATIONS OF COMPUTATIONAL MATHEMATICS.

Some structural results on D-n-finite functions

ADVANCES IN APPLIED MATHEMATICS, 117.

Walks in the quarter plane: Genus zero case

JOURNAL OF COMBINATORIAL THEORY SERIES A, 174.

Consistent systems of linear differential and difference equations

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 21(9), 2751–2792.

On the nature of the generating series of walks in the quarter plane

INVENTIONES MATHEMATICAE, 213(1), 139–203.

Galois groups for integrable and projectively integrable linear difference equations

JOURNAL OF ALGEBRA, 480, 423–449.

Desingularization of Ore operators

JOURNAL OF SYMBOLIC COMPUTATION, 74, 617–626.

Reductive Linear Differential Algebraic Groups and the Galois Groups of Parameterized Linear Differential Equations

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2015(7), 1733–1793.

On the summability of bivariate rational functions

JOURNAL OF ALGEBRA, 409, 320–343.

UNIPOTENT DIFFERENTIAL ALGEBRAIC GROUPS AS PARAMETERIZED DIFFERENTIAL GALOIS GROUPS

JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, 13(4), 671–700.

Linear algebraic groups as parameterized Picard-Vessiot Galois groups

JOURNAL OF ALGEBRA, 373, 153–161.

PROJECTIVE ISOMONODROMY AND GALOIS GROUPS

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 141(2), 605–617.

Monodromy groups of parameterized linear differential equations with regular singularities

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 44, 913–930.

Residues and telescopers for bivariate rational functions

ADVANCES IN APPLIED MATHEMATICS, 49(2), 111–133.

A Jordan-Holder Theorem for differential algebraic groups

JOURNAL OF ALGEBRA, 328(1), 190–217.

An algorithm to compute Liouvillian solutions of prime order linear difference-differential equations

Journal of Symbolic Computation, 45(3), 306–323.

Liouvillian solutions of linear difference-differential equations

JOURNAL OF SYMBOLIC COMPUTATION, 45(3), 287–305.

Differential Galois theory of linear difference equations

MATHEMATISCHE ANNALEN, 342(2), 333–377.

Model theory of partial differential fields: From commuting to noncommuting derivations

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 135(6), 1929–1934.

On the constructive inverse problem in differential Galois theory

COMMUNICATIONS IN ALGEBRA, 33(10), 3639–3665.

Linear differential operators for polynomial equations

Cormier, O., Singer, M. F., Trager, B. M., & Ulmer, F. (2002, November). JOURNAL OF SYMBOLIC COMPUTATION, Vol. 34, pp. 355–398.

Effective methods in algebraic geometry

Singer, M. F. (2001, October 24). JOURNAL OF PURE AND APPLIED ALGEBRA, Vol. 164, pp. 1–2.

Calculating the Galois group of L-1(L-2(y))=0, L-1,L-2 completely reducible operators

Berman, P. H., & Singer, M. F. (1999, June 17). JOURNAL OF PURE AND APPLIED ALGEBRA, Vol. 139, pp. 3–23.

Computing Galois groups of completely reducible differential equations

JOURNAL OF SYMBOLIC COMPUTATION, 28(4-5), 473–494.

Solving difference equations in finite terms

JOURNAL OF SYMBOLIC COMPUTATION, 27(3), 239–259.

Linear differential equations and products of linear forms

Singer, M. F., & Ulmer, F. (1997, May). JOURNAL OF PURE AND APPLIED ALGEBRA, Vol. 117, pp. 549–563.