Michael Singer

Chen, S., Feng, R., Li, Z., Singer, M. F., & Watt, S. M. (2024). Telescopers for differential forms with one parameter. SELECTA MATHEMATICA-NEW SERIES, 30(3). https://doi.org/10.1007/s00029-024-00926-6

Raab, C. G., & Singer, M. F. (Eds.). (2022). Integration in Finite Terms: Fundamental Sources. https://doi.org/10.1007/978-3-030-98767-1

Hardouin, C., & Singer, M. F. (2021). On differentially algebraic generating series for walks in the quarter plane. SELECTA MATHEMATICA-NEW SERIES, 27(5). https://doi.org/10.1007/s00029-021-00703-9

Dreyfus, T., Hardouin, C., Roques, J., & Singer, M. F. (2021). 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. https://doi.org/10.1007/978-3-030-84304-5_3

Hubert, E., & Singer, M. F. (2021, September 9). Sparse Interpolation in Terms of Multivariate Chebyshev Polynomials. FOUNDATIONS OF COMPUTATIONAL MATHEMATICS. https://doi.org/10.1007/s10208-021-09535-7

Jimenez-Pastor, A., Pillwein, V., & Singer, M. F. (2020). Some structural results on D-n-finite functions. ADVANCES IN APPLIED MATHEMATICS, 117. https://doi.org/10.1016/j.aam.2020.102027

Dreyfus, T., Hardouin, C., Roques, J., & Singer, M. F. (2020). Walks in the quarter plane: Genus zero case. JOURNAL OF COMBINATORIAL THEORY SERIES A, 174. https://doi.org/10.1016/j.jcta.2020.105251

Schafke, R., & Singer, M. F. (2019). Consistent systems of linear differential and difference equations. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 21(9), 2751–2792. https://doi.org/10.4171/JEMS/891

Dreyfus, T., Hardouin, C., Roques, J., & Singer, M. F. (2018). On the nature of the generating series of walks in the quarter plane. INVENTIONES MATHEMATICAE, 213(1), 139–203. https://doi.org/10.1007/s00222-018-0787-z

Arreche, C. K., & Singer, M. F. (2017). Galois groups for integrable and projectively integrable linear difference equations. JOURNAL OF ALGEBRA, 480, 423–449. https://doi.org/10.1016/j.jalgebra.2017.02.032

Chen, S., Kauers, M., & Singer, M. F. (2016). Desingularization of Ore operators. JOURNAL OF SYMBOLIC COMPUTATION, 74, 617–626. https://doi.org/10.1016/j.jsc.2015.11.001

Minchenko, A., Ovchinnikov, A., & Singer, M. F. (2015). Reductive Linear Differential Algebraic Groups and the Galois Groups of Parameterized Linear Differential Equations. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2015(7), 1733–1793. https://doi.org/10.1093/imrn/rnt344

Chen, S., & Singer, M. F. (2014). On the summability of bivariate rational functions. JOURNAL OF ALGEBRA, 409, 320–343. https://doi.org/10.1016/j.jalgebra.2014.03.023

Minchenko, A., Ovchinnikov, A., & Singer, M. F. (2014). UNIPOTENT DIFFERENTIAL ALGEBRAIC GROUPS AS PARAMETERIZED DIFFERENTIAL GALOIS GROUPS. JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, 13(4), 671–700. https://doi.org/10.1017/s1474748013000200

Singer, M. F. (2013). Linear algebraic groups as parameterized Picard-Vessiot Galois groups. JOURNAL OF ALGEBRA, 373, 153–161. https://doi.org/10.1016/j.jalgebra.2012.09.037

Mitschi, C., & Singer, M. F. (2013). PROJECTIVE ISOMONODROMY AND GALOIS GROUPS. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 141(2), 605–617. https://doi.org/10.1090/s0002-9939-2012-11499-6

Mitschi, C., & Singer, M. F. (2012). Monodromy groups of parameterized linear differential equations with regular singularities. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 44, 913–930. https://doi.org/10.1112/blms/bds021

Chen, S., & Singer, M. F. (2012). Residues and telescopers for bivariate rational functions. ADVANCES IN APPLIED MATHEMATICS, 49(2), 111–133. https://doi.org/10.1016/j.aam.2012.04.003

Cassidy, P. J., & Singer, M. F. (2011). A Jordan-Holder Theorem for differential algebraic groups. JOURNAL OF ALGEBRA, 328(1), 190–217. https://doi.org/10.1016/j.jalgebra.2010.08.019

Feng, R. Y., Singer, M. F., & Wu, M. (2010). An algorithm to compute Liouvillian solutions of prime order linear difference-differential equations. Journal of Symbolic Computation, 45(3), 306–323. https://doi.org/10.1016/j.jsc.2009.09.002

Feng, R., Singer, M. F., & Wu, M. (2010). Liouvillian solutions of linear difference-differential equations. JOURNAL OF SYMBOLIC COMPUTATION, 45(3), 287–305. https://doi.org/10.1016/j.jsc.2009.09.001

Hardouin, C., & Singer, M. F. (2008). Differential Galois theory of linear difference equations. MATHEMATISCHE ANNALEN, 342(2), 333–377. https://doi.org/10.1007/s00208-008-0238-z

Singer, M. F. (2007). Model theory of partial differential fields: From commuting to noncommuting derivations. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 135(6), 1929–1934. https://doi.org/10.1090/S0002-9939-07-08653-4

Cook, W. J., Mitschi, C., & Singer, M. F. (2005). On the constructive inverse problem in differential Galois theory. COMMUNICATIONS IN ALGEBRA, 33(10), 3639–3665. https://doi.org/10.1080/00927870500243304

Cormier, O., Singer, M. F., Trager, B. M., & Ulmer, F. (2002, November). Linear differential operators for polynomial equations. JOURNAL OF SYMBOLIC COMPUTATION, Vol. 34, pp. 355–398. https://doi.org/10.1006/jsco.2002.0564

Singer, M. F. (2001, October 24). Effective methods in algebraic geometry. JOURNAL OF PURE AND APPLIED ALGEBRA, Vol. 164, pp. 1–2. https://doi.org/10.1016/S0022-4049(00)00141-9

Berman, P. H., & Singer, M. F. (1999, June 17). Calculating the Galois group of L-1(L-2(y))=0, L-1,L-2 completely reducible operators. JOURNAL OF PURE AND APPLIED ALGEBRA, Vol. 139, pp. 3–23. https://doi.org/10.1016/S0022-4049(99)00003-1

Compoint, E., & Singer, M. F. (1999). Computing Galois groups of completely reducible differential equations. JOURNAL OF SYMBOLIC COMPUTATION, 28(4-5), 473–494. https://doi.org/10.1006/jsco.1999.0311

Hendriks, P. A., & Singer, M. F. (1999). Solving difference equations in finite terms. JOURNAL OF SYMBOLIC COMPUTATION, 27(3), 239–259. https://doi.org/10.1006/jsco.1998.0251

Singer, M. F., & Ulmer, F. (1997, May). Linear differential equations and products of linear forms. JOURNAL OF PURE AND APPLIED ALGEBRA, Vol. 117, pp. 549–563. https://doi.org/10.1016/S0022-4049(97)00027-3