Michael F. Singer | Academic Influence

Michael F. Singer's AcademicInfluence.com Rankings

Michael F. Singer

Mathematics

#5300

World Rank

#7470

Historical Rank

#1757

USA Rank

Measure Theory

#2537

World Rank

#3045

Historical Rank

#718

USA Rank

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Mathematics

Michael F. Singer's Degrees

PhD Mathematics University of California, Berkeley
Bachelors Mathematics University of California, Berkeley

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Why Is Michael F. Singer Influential?

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According to Wikipedia, Michael F. Singer is an American mathematician. Singer graduated from New York University with a bachelor's degree in 1970 and from the University of California, Berkeley with a master's degree in 1972 and a doctorate in 1974 under the supervision of Maxwell Rosenlicht with thesis Functions Satisfying Elementary Relations. From 1974 to 1976 Singer was an instructor at the State University of New York at Stony Brook . At North Carolina State University he was from 1974 to 1976 an assistant professor, from 1976 to 1982 an associate professor, and from 1986 to 2016 a full professor, retiring as professor emeritus in 2016.

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Michael F. Singer's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Galois Theory of Linear Differential Equations (2012) (626)
Spectral asymmetry and Riemannian geometry. II (1975) (476)
Elementary first integrals of differential equations (1981) (307)
Galois Theory of Difference Equations (1997) (278)
Liouvillian First Integrals of Differential Equations (1988) (257)
Differential Galois theory of linear difference equations (2008) (140)
Galois Groups of Second and Third Order Linear Differential Equations (1993) (139)
Fast Parallel Algorithms for Sparse Multivariate Polynomial Interpolation over Finite Fields (1988) (136)
Liouvillian Solutions of n-th Order Homogeneous Linear Differential Equations (1981) (134)
Solving Difference Equations in Finite Terms (1999) (120)
Liouvillian and Algebraic Solutions of Second and Third Order Linear Differential Equations (1993) (99)
Liouvillian Solutions of Linear Differential Equations with Liouvillian Coefficients (1989) (96)
Testing reducibility of linear differential operators: A group theoretic perspective (1996) (95)
Galois Theory of Parameterized Differential Equations and Linear Differential Algebraic Groups (2005) (80)
Extremal metrics on blowups (2006) (67)
Existence and deformation theory for scalar-flat Kähler metrics on compact complex surfaces (1993) (67)
A Kummer-type construction of self-dual 4-manifolds (1994) (66)
The model theory of ordered differential fields (1978) (60)
Formal Solutions of Differential Equations (1990) (59)
Solving ordinary differential equations in terms of series with real exponents (1991) (56)
On the nature of the generating series of walks in the quarter plane (2017) (55)
Solving homogeneous linear differential equations in terms of second order linear differential equations (1985) (54)
On the infinitesimal geometry of integrable systems (1992) (53)
An extension of Liouville's theorem on integration in finite terms (1981) (51)
Telescopers for rational and algebraic functions via residues (2012) (46)
Computing Galois Groups of Completely Reducible Differential Equations (1999) (44)
Algebraic Relations Among Solutions of Linear Differential Equations: Fano's Theorem (1988) (43)
Connected Linear Groups as Differential Galois Groups (1996) (42)
Extremal metrics on blow ups (2006) (42)
Linear differential equations and products of linear forms (1997) (41)
Residues and telescopers for bivariate rational functions (2012) (41)
A differentially algebraic elimination theorem with application to analog computability in the calculus of variations (1985) (41)
Computational Complexity of Sparse Rational Interpolation (1994) (40)
Algebraic relations among solutions of linear di erential equations (1986) (39)
Moduli of linear differential equations on the Riemann sphere with fixed Galois groups (1993) (38)
Model Theory with Applications to Algebra and Analysis: On the definitions of difference Galois groups (2007) (37)
Necessary conditions for liouvillian solutions of (third order) linear differential equations (2005) (37)
Desingularization explains order-degree curves for ore operators (2013) (35)
Unipotent differential algebraic groups as parameterized differential Galois groups (2013) (34)
Reductive Linear Differential Algebraic Groups and the Galois Groups of Parameterized Linear Differential Equations (2013) (33)
Introduction to the Galois Theory of Linear Differential Equations (2007) (32)
Linear Differential Operators for Polynomial Equations (2002) (32)
Positive Einstein metrics with small Ln/2-norm of the Weyl tensor (1992) (31)
Group-theoretic obstructions to integrability (1995) (30)
A Jordan–Hölder Theorem for differential algebraic groups (2010) (30)
Monodromy groups of parameterized linear differential equations with regular singularities (2011) (30)
Linear algebraic groups as parameterized Picard-Vessiot Galois groups (2011) (29)
Calculating the Galois group of L1(L2(y))=0,L1,L2 completely reducible operators (1999) (28)
The Interpolation Problem for k-sparse Sums of Eigenfunctions of Operators (1991) (28)
Interpolation of sparse rational functions without knowing bounds on exponents (1990) (24)
Desingularization of Ore operators (2014) (23)
Consistent systems of linear differential and difference equations (2016) (21)
A class of differential fields with minimal differential closures (1978) (20)
Differential equations and computer algebra (1991) (20)
Walks in the quarter plane: Genus zero case (2017) (19)
Galois Theories of Linear Difference Equations: An Introduction (2016) (19)
Solvable-by-finite groups as differential Galois groups(*) (2002) (18)
On elementary, generalized elementary, and liouvillian extension fields (1977) (18)
Elementary and Liouvillian Solutions of Linear Differential Equations (1985) (17)
Planar polynomial foliations (1980) (16)
ELEMENTARY SOLUTIONS OF DIFFERENTIAL EQUATIONS (1975) (15)
Algebraic properties of the ring of general exponential polynomials (1989) (14)
Galois groups for integrable and projectively integrable linear difference equations (2016) (14)
Projective isomonodromy and Galois groups (2010) (13)
On the Summability of Bivariate Rational Functions (2012) (13)
A recursive method for determining the one-dimensional submodules of Laurent-Ore modules (2006) (13)
Liouvillian solutions of linear difference-differential equations (2008) (13)
A class of vectorfields on S2 that are topologically equivalent to polynomial vectorfields (1985) (12)
Computational Complexity of Sparse Real Algebraic Function Interpolation (1992) (12)
Functions satisfying elementary relations (1977) (11)
Partial Compactification of Monopoles and Metric Asymptotics (2015) (11)
THE SPACE OF HYPERKÄHLER METRICS ON A 4-MANIFOLD WITH BOUNDARY (2016) (11)
An algorithm to compute Liouvillian solutions of prime order linear difference-differential equations (2010) (10)
Solutions of linear differential equations in function fields of one variable (1976) (10)
Scattering configuration spaces (2008) (10)
Separatrices at singular points of planar vector fields (1980) (9)
Parallel telescoping and parameterized Picard-Vessiot theory (2014) (8)
Size Efficient Parallel Algebraic Circuits for Partial Derivatives * (2008) (8)
Model theory of partial differential fields: From commuting to noncommuting derivations (2006) (8)
On differentially algebraic generating series for walks in the quarter plane (2020) (8)
Liouvillian solutions of third order linear differential equations: new bounds and necessary conditions (1992) (8)
On a Third Order Differential Equation whose Differential Galois Group is the Simple Group of 168 Elements (1993) (7)
Some structural results on Dn-finite functions (2020) (7)
On the Constructive Inverse Problem in Differential Galois Theory (2004) (6)
Unipotent dierential algebraic groups as parameterized dierential Galois groups (2013) (6)
Singular points of planar vector fields (1980) (6)
On Computing Algebraic Functions Using Logarithms and Exponentials (1995) (6)
Algebraic and algorithmic aspects of linear difference equations (2016) (5)
A Classification of Differential Equations of Fuchsian Class (1985) (5)
On Ramis's solution of the local inverse problem of differential Galois theory (1996) (5)
Computing galois groups for certain classes of ordinary differential equations (2001) (5)
Computing the Galois group of a polynomial using linear differential equations (2000) (5)
Some remarks on conic degeneration and bending of Poincaré-Einstein metrics (2007) (5)
Computing galois groups of linear differential equations of order four (1997) (4)
Monopoles and the Sen Conjecture: Part I (2018) (4)
Dk Gravitational Instantons as Superpositions of Atiyah–Hitchin and Taub–NUT Geometries (2020) (4)
Direct and Inverse Problems in Diierential Galois Theory (1997) (3)
Mahler equations and rationality (2016) (3)
Some Applications of Linear Groups to Differential Equations (1985) (3)
The Inverse Problem in Di erential Galois Theory (1996) (3)
On the Kernel Curves Associated with Walks in the Quarter Plane (2020) (3)
The inverse problem for difference equations (1997) (3)
Local rigidity of Einstein 4-manifolds satisfying a chiral curvature condition (2019) (3)
On the nature of the generating series of walks in the quarter plane (2018) (2)
Addendum to: “Planar polynomial foliations” (1981) (2)
Remarks on Analytic Continuation (1980) (2)
Sparse Interpolation in Terms of Multivariate Chebyshev Polynomials (2020) (2)
Liouvillian Solutions of Difference-Differential Equations (2008) (2)
East Coast Computer Algebra Day '99 (April 24, 1999): abstracts of invited talks and presented posters (1999) (1)
Picard-Vessiot Theory (2003) (1)
Algebraic and Algorithmic Aspects of Difference Equations (2012) (1)
Erratum to: Separatrices at singular points of planar vector fields (1983) (1)
Telescopers for differential forms with one parameter (2021) (1)
Monodromy, the Riemann-Hilbert Problem, and the Differential Galois Group (2003) (1)
Erratum to: Differential Galois theory of linear difference equations (2011) (1)
Separability Problems in Creative Telescoping (2021) (1)
Galois Theory of Parameterized Dierential Equations (2005) (1)
Formal Local Theory (2003) (0)
On the algebraic dependence of holonomic functions (2020) (0)
Differential Equations on the Complex Sphere and the Riemann-Hilbert Problem (2003) (0)
Classification and canonical forms (1997) (0)
Wild difference equations (1997) (0)
Stokes Phenomenon and Differential Galois Groups (2003) (0)
Difference modules over \(\mathcal{P}\) (1997) (0)
A pr 2 01 3 Reductive linear differential algebraic groups and the Galois groups of parameterized linear differential equations (2013) (0)
q -difference equations (1997) (0)
Book Review: Algorithms in Real Algebraic Geometry (2007) (0)
Differential Operators and Differential Modules (2003) (0)
An excursion in positive characteristic (1997) (0)
DIFFERENTIAL EQUATIONS: FANO'S THEOREM (2016) (0)
Algorithms for difference equations (1997) (0)
Semi-regular difference equations (1997) (0)
LIOUVILLIAN SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS WITH LIOUVILLIAN COEFFICmNTS Extended Abstract (1989) (0)
Universal Picard-Vessiot Rings and Galois Groups (2003) (0)
ON THE ALGEBRAIC DEPENDENCE OF HOLONOMIC FUNCTIONS SUR LA DÉPENDANCE ALGÉBRIQUE DES FONCTIONS HOLONOMES (2022) (0)
Remarks on the Period Mapping for 4-Dimensional Conformal Structures (2017) (0)
Residues and Telescopers for Rational Functions (2012) (0)
4. MSRI Addresses the Challenge by Hélène Barcelo and Michael F. Singer (2022) (0)
Galois Theory of Linear Differential Equations - ReadingSample (2017) (0)
Moduli for Singular Differential Equations (2003) (0)
The ring S of sequences (1997) (0)
EQUATIONS IN TERMS OF SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS (2016) (0)
Examples of equations and galois groups (1997) (0)
Mild difference equations (1997) (0)
Weak Solutions of the Cohomological Equation on R 2 for Regular Vector Fields (2016) (0)
Stokes Matrices and Meromorphic Classification (2003) (0)
PARAMETERIZED LINEAR DIFFERENTIAL EQUATIONS WITH REGULAR SINGULARITIES (2011) (0)
Connected Linear Groups as Differential Galois Groups over $C(x)$. (1995) (0)
Picard-Vessiot rings (1997) (0)
Book Review: Algorithms in Real Algebraic Geometry by S. Basu, R. Pollack, and M.-F. Roy (2007) (0)
On the integer zeros of exponential polynomials (1993) (0)

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