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Abramov, Sergeĭ Aleksandrovich

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Author ID: abramov.sergei-a Recent zbMATH articles by "Abramov, Sergeĭ Aleksandrovich"
Published as: Abramov, S. A.; Abramov, Sergei A.; Abramov, Sergei; Abramov, Sergey A.; Abramov, S.
Homepage: http://www.ccas.ru/sabramov/
External Links: MGP · Wikidata · ResearchGate · Math-Net.Ru
Documents Indexed: 158 Publications since 1971, including 1 Book
2 Contributions as Editor
Biographic References: 2 Publications
Co-Authors: 35 Co-Authors with 92 Joint Publications
574 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

96 Publications have been cited 692 times in 232 Documents Cited by Year
Rational solutions of linear differential and difference equations with polynomial coefficients. Zbl 0719.65063
Abramov, S. A.
29
1989
\(q\)-hypergeometric solutions of \(q\)-difference equations. Zbl 0932.33019
Abramov, Sergei A.; Paule, Peter; Petkovšek, Marko
29
1998
On polynomial solutions of linear operator equations. Zbl 0914.65132
Abramov, Sergei A.; Bronstein, Manuel; Petkovšek, Marko
25
1995
EG-eliminations. Zbl 0936.65144
Abramov, Sergei A.
23
1999
Rational solutions of first order linear difference systems. Zbl 0919.65089
Abramov, S. A.; Barkatou, M. A.
22
1998
D’Alembertian solutions to linear differential and difference equations. Zbl 0919.34013
Abramov, Sergei A.; Petkovšek, Marko
22
1994
On solutions of linear functional systems. Zbl 1356.65245
Abramov, Sergei A.; Bronstein, Manuel
22
2001
Rational normal forms and minimal decompositions of hypergeometric terms. Zbl 1005.33010
Abramov, S. A.; Petkovšek, M.
18
2002
Rational solutions of linear differential and difference equations with polynomial coefficients. Zbl 0695.65051
Abramov, S. A.
18
1989
Indefinite sums of rational functions. Zbl 0914.65133
Abramov, S. A.
18
1995
Rational solutions of linear difference and \(q\)-differential equations with polynomial coefficients. Zbl 0910.65107
Abramov, S. A.
17
1995
When does Zeilberger’s algorithm succeed? Zbl 1030.33011
Abramov, S. A.
16
2003
Rationale Komponente der Lösung einer linearen rekurrenten Relation erster Ordnung mit rationaler rechter Seite. Zbl 0326.65069
Abramov, S. A.
16
1975
A criterion for the applicability of Zeilberger’s algorithm to rational functions. Zbl 1023.33017
Abramov, S. A.; Le, H. Q.
12
2002
On singular points of solutions of linear differential systems with polynomial coefficients. Zbl 1258.34027
Abramov, S. A.; Khmelnov, D. E.
12
2012
Über die Summation rationaler Funktionen. Zbl 0243.65076
Abramov, S. A.
12
1971
On the structure of multivariate hypergeometric terms. Zbl 1057.33017
Abramov, S. A.; Petkovšek, M.
11
2002
Rational solutions of linear difference and \(q\)-difference equations with polynomial coefficients. Zbl 0914.65131
Abramov, S. A.
11
1995
Integration of solutions of linear functional equations. Zbl 0939.34059
Abramov, Sergei A.; van Hoeij, Mark
11
1999
Factorization of polynomials and GCD computations for finding universal denominators. Zbl 1202.12004
Abramov, S. A.; Gheffar, A.; Khmelnov, D. E.
11
2010
On full rank differential systems with power series coefficients. Zbl 1308.34019
Abramov, S. A.; Barkatou, M. A.; Khmelnov, D. E.
10
2015
Rational solutions of linear difference equations: universal denominators and denominator bounds. Zbl 1247.65156
Abramov, S. A.; Gheffar, A.; Khmelnov, D. E.
10
2011
On regular and logarithmic solutions of ordinary linear differential systems. Zbl 1169.34301
Abramov, S. A.; Bronstein, M.; Khmelnov, D. E.
10
2005
On the dimension of solution spaces of full rank linear differential systems. Zbl 1412.34055
Abramov, S. A.; Barkatou, M. A.
9
2013
Linear differential and difference systems: \(\mathrm{EG}_\delta\)- and \(\mathrm{EG}_\sigma\)-eliminations. Zbl 1311.34027
Abramov, S. A.; Khmelnov, D. E.
9
2013
Valuations of rational solutions of linear difference equations at irreducible polynomials. Zbl 1221.68298
Gheffar, A.; Abramov, S.
9
2011
Higher-order linear differential systems with truncated coefficients. Zbl 1344.68290
Abramov, S. A.; Barkatou, M. A.; Pflügel, E.
9
2011
Special formal series solutions of linear operator equations. Zbl 0972.34002
Abramov, Sergei A.; Petkovšek, Marko; Ryabenko, Anna
9
2000
Applicability of Zeilberger’s algorithm to hypergeometric terms. Zbl 1072.68642
Abramov, S. A.
9
2002
Denominators of rational solutions of linear difference systems of an arbitrary order. Zbl 1261.65134
Abramov, S. A.; Khmelnov, D. E.
9
2012
On the summation of rational functions. Zbl 0255.65003
Abramov, S. A.
8
1973
D’Alembertian solutions of inhomogeneous linear equations (differential, difference, and some other). Zbl 0966.34005
Abramov, Sergei A.; Zima, Eugene V.
8
1996
Ore polynomial rings in one variable in computer algebra. Zbl 1127.16302
Abramov, S. A.; Le, H. Q.; Li, Z.
8
2005
Telescoping in the context of symbolic summation in Maple. Zbl 1137.05326
Abramov, S. A.; Carette, J. J.; Geddes, K. O.; Le, H. Q.
8
2005
Apparent singularities of linear difference equations with polynomial coefficients. Zbl 1106.39002
Abramov, S. A.; Barkatou, M. A.; van Hoeij, M.
7
2006
Problems of computer algebra connected with the search for polynomial solutions of linear differential and difference equations. Zbl 0689.65049
Abramov, S. A.
7
1989
Principles of inverse computation and the universal resolving algorithm. Zbl 1026.68023
Abramov, Sergei; Glück, Robert
7
2002
On polynomial solutions of linear partial differential and \((q\)-)difference equations. Zbl 1373.68458
Abramov, S. A.; Petkovšek, M.
7
2012
Solving linear systems of differential and difference equations with respect to a part of the unknowns. Zbl 1179.65100
Abramov, S. A.; Bronstein, M.
7
2006
Minimal decomposition of indefinite hypergeometric sums. Zbl 1356.33012
Abramov, Sergei A.; Petkovsek, M.
7
2001
Applicability of Zeilberger’s algorithm to rational functions. Zbl 0963.65026
Abramov, S. A.; Le, H. Q.
6
2000
On solution spaces of products of linear differential or difference operators. Zbl 1322.68269
Abramov, Sergei A.; Barkatou, Moulay A.
6
2014
Regular solutions of linear differential systems with power series coefficients. Zbl 1317.34019
Abramov, S. A.; Khmelnov, D. E.
6
2014
Fast algorithms to search for the rational solutions of linear differential equations with polynomial coefficients. Zbl 0919.65045
Abramov, S. A.; Kvansenko, K. Yu.
6
1991
Analytic solutions of linear difference equations, formal series, and bottom summation. Zbl 1141.68663
Abramov, S. A.; Petkovšek, M.
6
2007
Polynomial ring automorphisms, rational \((w,\sigma )\)-canonical forms, and the assignment problem. Zbl 1189.33038
Abramov, S. A.; Petkovšek, M.
6
2010
Computable infinite power series in the role of coefficients of linear differential systems. Zbl 1416.68211
Abramov, Sergei A.; Barkatou, Moulay A.
6
2014
Search of rational solutions to differential and difference systems by means of formal series. Zbl 1344.34023
Abramov, Sergey A.
6
2015
On the differential and full algebraic complexities of operator matrices transformations. Zbl 1453.34014
Abramov, Sergei A.
6
2016
Hypergeometric dispersion and the orbit problem. Zbl 1326.68340
Abramov, Sergei A.; Bronstein, Manuel
5
2000
The universal resolving algorithm and its correctness: Inverse computation in a functional language. Zbl 1014.68037
Abramov, Sergei; Glück, Robert
5
2002
The universal resolving algorithm: Inverse computation in a functional language. Zbl 0963.68500
Abramov, Sergei; Glück, Robert
5
2000
Gosper’s algorithm, accurate summation, and the discrete Newton-Leibniz formula. Zbl 1360.33018
Abramov, S. A.; Petkovšsek, M.
5
2005
A method for the integration of solutions to Ore equations. Zbl 0919.34011
Abramov, Sergei A.; van Hoeij, Mark
5
1997
Linear ordinary differential equations and truncated series. Zbl 1442.34033
Abramov, S. A.; Ryabenko, A. A.; Khmelnov, D. E.
5
2019
Problems of computer algebra involved in the search for polynomial solutions of linear differential and difference equations. Zbl 0723.65048
Abramov, S. A.
5
1989
Procedures for searching local solutions of linear differential systems with infinite power series in the role of coefficients. Zbl 1345.34011
Abramov, Sergey A.; Ryabenko, Anna A.; Khmelnov, Dennis E.
5
2016
Hypergeometric solutions of first-order linear difference systems with rational-function coefficients. Zbl 1434.33020
Abramov, S. A.; Petkovšek, M.; Ryabenko, A. A.
4
2015
A direct algorithm to compute rational solutions of first order linear \(q\)-difference systems. Zbl 0995.65139
Abramov, S. A.
4
2002
Subanalytic solutions of linear difference equations and multidimensional hypergeometric sequences. Zbl 1232.39001
Abramov, S. A.; Barkatou, M. A.; Van Hoeij, M.; Petkovšek, M.
4
2011
The research seminar on computer algebra in 2009-2010. Zbl 1242.00036
Abramov, S. A.; Bogolyubskaya, A. A.; Edneral, V. F.; Rostovtsev, V. A.
3
2011
The scientific research seminar on computer algebra in 1997-1998. Zbl 0972.68814
Abramov, S. A.; Rostovtsev, V. A.
3
1998
Computer algebra library for the construction of the minimal telescopers. Zbl 1012.68229
Abramov, S. A.; Geddes, K. O.; Le, H. Q.
3
2002
Minimal completely factorable annihilators. Zbl 0929.16045
Abramov, Sergei A.; Zima, Eugene
3
1997
On the greatest common divisor of polynomials which depend on a parameter. Zbl 0925.13009
Abramov, S. A.; Kvashenko, K. Yu.
3
1993
The set of poles of solutions of linear difference equations with polynomial coefficients. Zbl 1076.39002
Abramov, S. A.; van Hoeij, M.
3
2003
An universal resolving algorithm for inverse computation of lazy languages. Zbl 1185.68328
Abramov, Sergei; Glück, Robert; Klimov, Yuri
3
2007
Improved universal denominators. Zbl 1147.68877
Abramov, S. A.; Polyakov, S. P.
3
2007
Regular solutions of linear ordinary differential equations and truncated series. Zbl 1454.34026
Abramov, S. A.; Ryabenko, A. A.; Khmelnov, D. E.
3
2020
On the summation of \(P\)-recursive sequences. Zbl 1356.33011
Abramov, S. A.
3
2006
In memory of Manuel Bronstein. Zbl 1208.01020
Abramov, S. A.
2
2006
On valuations of meromorphic solutions of arbitrary-order linear difference systems with polynomial coefficients. Zbl 1323.68577
Abramov, S. A.; Khmelnov, D. E.
2
2012
Combining semantics with non-standard interpreter hierarchies. Zbl 1044.68664
Abramov, Sergei; Glück, Robert
2
2000
The rational component of the solution of a first-order linear recurrence relation with a rational right side. Zbl 0352.65062
Abramov, S. A.
2
1976
Rational canonical forms and efficient representations of hypergeometric terms. Zbl 1072.68643
Abramov, S. A.; Le, H. Q.; Petkovšek, M.
2
2003
The research seminar on computer algebra in 2005-2006. Zbl 1137.68300
Abramov, S. A.; Bogolyubskaya, A. A.; Rostovtsev, V. A.; Edneral, V. F.
2
2007
Resolving sequences of operators for linear ordinary differential and difference systems of arbitrary order. Zbl 1379.39001
Abramov, Sergey A.; Petkovšek, Marko; Ryabenko, Anna A.
2
2016
On rational and hypergeometric solutions of linear ordinary difference equations in \(\Pi\Sigma^\ast\)-field extensions. Zbl 07354271
Abramov, Sergei A.; Bronstein, Manuel; Petkovšek, Marko; Schneider, Carsten
2
2021
Indicial rational functions of linear ordinary differential equations with polynomial coefficients. Zbl 1288.34009
Abramov, S. A.; Ryabenko, A. A.
1
2009
Rational solutions of linear difference and \(q\)-difference equations with polynomial coefficients. Zbl 0972.68184
Abramov, S. A.
1
1999
On peripheral factorization of linear homogeneous operators. Zbl 0973.68667
Abramov, S. A.; Tsarev, S. P.
1
1997
From standard to non-standard semantics by semantics modifiers. Zbl 1319.68050
Abramov, Sergei; Glück, Robert
1
2001
On d’Alembert substitution. Zbl 0921.34011
Abramov, S. A.
1
1993
The denominators of rational solutions to linear difference equations. Zbl 0824.33013
Abramov, S. A.
1
1994
Inverse linear difference operators. Zbl 1386.15014
Abramov, S. A.
1
2017
The finite-difference second order equation with constant coefficients in the field of rational functions. Zbl 0369.39003
Abramov, S. A.
1
1977
On the order of the recurrence produced by the method of creative telescoping. Zbl 1077.33037
Abramov, S. A.; Le, H. Q.
1
2005
An algorithm for searching quasirational solutions of linear differential and difference equations with polynomial coefficients. Zbl 0727.65062
Abramov, S. A.
1
1991
Dimensions of solution spaces of \(H\)-systems. Zbl 1186.33038
Abramov, S. A.; Petkovšek, M.
1
2008
Matrices of scalar differential operators: divisibility and spaces of solutions. Zbl 07264245
Abramov, S. A.; Barkatou, M. A.; Petkovšek, M.
1
2020
Revealing matrices of linear differential systems of arbitrary order. Zbl 1455.34002
Abramov, S. A.; Ryabenko, A. A.; Khmelnov, D. E.
1
2017
Procedures for searching Laurent and regular solutions of linear differential equations with the coefficients in the form of truncated power series. Zbl 1462.34028
Abramov, S. A.; Ryabenko, A. A.; Khmelnov, D. E.
1
2020
Truncated series and formal exponential-logarithmic solutions of linear ordinary differential equations. Zbl 07282628
Abramov, S. A.; Ryabenko, A. A.; Khmelnov, D. E.
1
2020
On strongly non-singular polynomial matrices. Zbl 07008083
Abramov, Sergei A.; Barkatou, Moulay A.
1
2018
On \(m\)-interlacing solutions of linear difference equations. Zbl 1239.39001
Abramov, S. A.; Barkatou, M. A.; Khmelnov, D. E.
1
2009
On unimodular matrices of difference operators. Zbl 1453.65442
Abramov, S. A.; Khmelnov, D. E.
1
2018
On rational and hypergeometric solutions of linear ordinary difference equations in \(\Pi\Sigma^\ast\)-field extensions. Zbl 07354271
Abramov, Sergei A.; Bronstein, Manuel; Petkovšek, Marko; Schneider, Carsten
2
2021
Regular solutions of linear ordinary differential equations and truncated series. Zbl 1454.34026
Abramov, S. A.; Ryabenko, A. A.; Khmelnov, D. E.
3
2020
Matrices of scalar differential operators: divisibility and spaces of solutions. Zbl 07264245
Abramov, S. A.; Barkatou, M. A.; Petkovšek, M.
1
2020
Procedures for searching Laurent and regular solutions of linear differential equations with the coefficients in the form of truncated power series. Zbl 1462.34028
Abramov, S. A.; Ryabenko, A. A.; Khmelnov, D. E.
1
2020
Truncated series and formal exponential-logarithmic solutions of linear ordinary differential equations. Zbl 07282628
Abramov, S. A.; Ryabenko, A. A.; Khmelnov, D. E.
1
2020
Linear ordinary differential equations and truncated series. Zbl 1442.34033
Abramov, S. A.; Ryabenko, A. A.; Khmelnov, D. E.
5
2019
On strongly non-singular polynomial matrices. Zbl 07008083
Abramov, Sergei A.; Barkatou, Moulay A.
1
2018
On unimodular matrices of difference operators. Zbl 1453.65442
Abramov, S. A.; Khmelnov, D. E.
1
2018
Inverse linear difference operators. Zbl 1386.15014
Abramov, S. A.
1
2017
Revealing matrices of linear differential systems of arbitrary order. Zbl 1455.34002
Abramov, S. A.; Ryabenko, A. A.; Khmelnov, D. E.
1
2017
On the differential and full algebraic complexities of operator matrices transformations. Zbl 1453.34014
Abramov, Sergei A.
6
2016
Procedures for searching local solutions of linear differential systems with infinite power series in the role of coefficients. Zbl 1345.34011
Abramov, Sergey A.; Ryabenko, Anna A.; Khmelnov, Dennis E.
5
2016
Resolving sequences of operators for linear ordinary differential and difference systems of arbitrary order. Zbl 1379.39001
Abramov, Sergey A.; Petkovšek, Marko; Ryabenko, Anna A.
2
2016
On full rank differential systems with power series coefficients. Zbl 1308.34019
Abramov, S. A.; Barkatou, M. A.; Khmelnov, D. E.
10
2015
Search of rational solutions to differential and difference systems by means of formal series. Zbl 1344.34023
Abramov, Sergey A.
6
2015
Hypergeometric solutions of first-order linear difference systems with rational-function coefficients. Zbl 1434.33020
Abramov, S. A.; Petkovšek, M.; Ryabenko, A. A.
4
2015
On solution spaces of products of linear differential or difference operators. Zbl 1322.68269
Abramov, Sergei A.; Barkatou, Moulay A.
6
2014
Regular solutions of linear differential systems with power series coefficients. Zbl 1317.34019
Abramov, S. A.; Khmelnov, D. E.
6
2014
Computable infinite power series in the role of coefficients of linear differential systems. Zbl 1416.68211
Abramov, Sergei A.; Barkatou, Moulay A.
6
2014
On the dimension of solution spaces of full rank linear differential systems. Zbl 1412.34055
Abramov, S. A.; Barkatou, M. A.
9
2013
Linear differential and difference systems: \(\mathrm{EG}_\delta\)- and \(\mathrm{EG}_\sigma\)-eliminations. Zbl 1311.34027
Abramov, S. A.; Khmelnov, D. E.
9
2013
On singular points of solutions of linear differential systems with polynomial coefficients. Zbl 1258.34027
Abramov, S. A.; Khmelnov, D. E.
12
2012
Denominators of rational solutions of linear difference systems of an arbitrary order. Zbl 1261.65134
Abramov, S. A.; Khmelnov, D. E.
9
2012
On polynomial solutions of linear partial differential and \((q\)-)difference equations. Zbl 1373.68458
Abramov, S. A.; Petkovšek, M.
7
2012
On valuations of meromorphic solutions of arbitrary-order linear difference systems with polynomial coefficients. Zbl 1323.68577
Abramov, S. A.; Khmelnov, D. E.
2
2012
Rational solutions of linear difference equations: universal denominators and denominator bounds. Zbl 1247.65156
Abramov, S. A.; Gheffar, A.; Khmelnov, D. E.
10
2011
Valuations of rational solutions of linear difference equations at irreducible polynomials. Zbl 1221.68298
Gheffar, A.; Abramov, S.
9
2011
Higher-order linear differential systems with truncated coefficients. Zbl 1344.68290
Abramov, S. A.; Barkatou, M. A.; Pflügel, E.
9
2011
Subanalytic solutions of linear difference equations and multidimensional hypergeometric sequences. Zbl 1232.39001
Abramov, S. A.; Barkatou, M. A.; Van Hoeij, M.; Petkovšek, M.
4
2011
The research seminar on computer algebra in 2009-2010. Zbl 1242.00036
Abramov, S. A.; Bogolyubskaya, A. A.; Edneral, V. F.; Rostovtsev, V. A.
3
2011
Factorization of polynomials and GCD computations for finding universal denominators. Zbl 1202.12004
Abramov, S. A.; Gheffar, A.; Khmelnov, D. E.
11
2010
Polynomial ring automorphisms, rational \((w,\sigma )\)-canonical forms, and the assignment problem. Zbl 1189.33038
Abramov, S. A.; Petkovšek, M.
6
2010
Indicial rational functions of linear ordinary differential equations with polynomial coefficients. Zbl 1288.34009
Abramov, S. A.; Ryabenko, A. A.
1
2009
On \(m\)-interlacing solutions of linear difference equations. Zbl 1239.39001
Abramov, S. A.; Barkatou, M. A.; Khmelnov, D. E.
1
2009
Dimensions of solution spaces of \(H\)-systems. Zbl 1186.33038
Abramov, S. A.; Petkovšek, M.
1
2008
Analytic solutions of linear difference equations, formal series, and bottom summation. Zbl 1141.68663
Abramov, S. A.; Petkovšek, M.
6
2007
An universal resolving algorithm for inverse computation of lazy languages. Zbl 1185.68328
Abramov, Sergei; Glück, Robert; Klimov, Yuri
3
2007
Improved universal denominators. Zbl 1147.68877
Abramov, S. A.; Polyakov, S. P.
3
2007
The research seminar on computer algebra in 2005-2006. Zbl 1137.68300
Abramov, S. A.; Bogolyubskaya, A. A.; Rostovtsev, V. A.; Edneral, V. F.
2
2007
Apparent singularities of linear difference equations with polynomial coefficients. Zbl 1106.39002
Abramov, S. A.; Barkatou, M. A.; van Hoeij, M.
7
2006
Solving linear systems of differential and difference equations with respect to a part of the unknowns. Zbl 1179.65100
Abramov, S. A.; Bronstein, M.
7
2006
On the summation of \(P\)-recursive sequences. Zbl 1356.33011
Abramov, S. A.
3
2006
In memory of Manuel Bronstein. Zbl 1208.01020
Abramov, S. A.
2
2006
On regular and logarithmic solutions of ordinary linear differential systems. Zbl 1169.34301
Abramov, S. A.; Bronstein, M.; Khmelnov, D. E.
10
2005
Ore polynomial rings in one variable in computer algebra. Zbl 1127.16302
Abramov, S. A.; Le, H. Q.; Li, Z.
8
2005
Telescoping in the context of symbolic summation in Maple. Zbl 1137.05326
Abramov, S. A.; Carette, J. J.; Geddes, K. O.; Le, H. Q.
8
2005
Gosper’s algorithm, accurate summation, and the discrete Newton-Leibniz formula. Zbl 1360.33018
Abramov, S. A.; Petkovšsek, M.
5
2005
On the order of the recurrence produced by the method of creative telescoping. Zbl 1077.33037
Abramov, S. A.; Le, H. Q.
1
2005
When does Zeilberger’s algorithm succeed? Zbl 1030.33011
Abramov, S. A.
16
2003
The set of poles of solutions of linear difference equations with polynomial coefficients. Zbl 1076.39002
Abramov, S. A.; van Hoeij, M.
3
2003
Rational canonical forms and efficient representations of hypergeometric terms. Zbl 1072.68643
Abramov, S. A.; Le, H. Q.; Petkovšek, M.
2
2003
Rational normal forms and minimal decompositions of hypergeometric terms. Zbl 1005.33010
Abramov, S. A.; Petkovšek, M.
18
2002
A criterion for the applicability of Zeilberger’s algorithm to rational functions. Zbl 1023.33017
Abramov, S. A.; Le, H. Q.
12
2002
On the structure of multivariate hypergeometric terms. Zbl 1057.33017
Abramov, S. A.; Petkovšek, M.
11
2002
Applicability of Zeilberger’s algorithm to hypergeometric terms. Zbl 1072.68642
Abramov, S. A.
9
2002
Principles of inverse computation and the universal resolving algorithm. Zbl 1026.68023
Abramov, Sergei; Glück, Robert
7
2002
The universal resolving algorithm and its correctness: Inverse computation in a functional language. Zbl 1014.68037
Abramov, Sergei; Glück, Robert
5
2002
A direct algorithm to compute rational solutions of first order linear \(q\)-difference systems. Zbl 0995.65139
Abramov, S. A.
4
2002
Computer algebra library for the construction of the minimal telescopers. Zbl 1012.68229
Abramov, S. A.; Geddes, K. O.; Le, H. Q.
3
2002
On solutions of linear functional systems. Zbl 1356.65245
Abramov, Sergei A.; Bronstein, Manuel
22
2001
Minimal decomposition of indefinite hypergeometric sums. Zbl 1356.33012
Abramov, Sergei A.; Petkovsek, M.
7
2001
From standard to non-standard semantics by semantics modifiers. Zbl 1319.68050
Abramov, Sergei; Glück, Robert
1
2001
Special formal series solutions of linear operator equations. Zbl 0972.34002
Abramov, Sergei A.; Petkovšek, Marko; Ryabenko, Anna
9
2000
Applicability of Zeilberger’s algorithm to rational functions. Zbl 0963.65026
Abramov, S. A.; Le, H. Q.
6
2000
Hypergeometric dispersion and the orbit problem. Zbl 1326.68340
Abramov, Sergei A.; Bronstein, Manuel
5
2000
The universal resolving algorithm: Inverse computation in a functional language. Zbl 0963.68500
Abramov, Sergei; Glück, Robert
5
2000
Combining semantics with non-standard interpreter hierarchies. Zbl 1044.68664
Abramov, Sergei; Glück, Robert
2
2000
EG-eliminations. Zbl 0936.65144
Abramov, Sergei A.
23
1999
Integration of solutions of linear functional equations. Zbl 0939.34059
Abramov, Sergei A.; van Hoeij, Mark
11
1999
Rational solutions of linear difference and \(q\)-difference equations with polynomial coefficients. Zbl 0972.68184
Abramov, S. A.
1
1999
\(q\)-hypergeometric solutions of \(q\)-difference equations. Zbl 0932.33019
Abramov, Sergei A.; Paule, Peter; Petkovšek, Marko
29
1998
Rational solutions of first order linear difference systems. Zbl 0919.65089
Abramov, S. A.; Barkatou, M. A.
22
1998
The scientific research seminar on computer algebra in 1997-1998. Zbl 0972.68814
Abramov, S. A.; Rostovtsev, V. A.
3
1998
A method for the integration of solutions to Ore equations. Zbl 0919.34011
Abramov, Sergei A.; van Hoeij, Mark
5
1997
Minimal completely factorable annihilators. Zbl 0929.16045
Abramov, Sergei A.; Zima, Eugene
3
1997
On peripheral factorization of linear homogeneous operators. Zbl 0973.68667
Abramov, S. A.; Tsarev, S. P.
1
1997
D’Alembertian solutions of inhomogeneous linear equations (differential, difference, and some other). Zbl 0966.34005
Abramov, Sergei A.; Zima, Eugene V.
8
1996
On polynomial solutions of linear operator equations. Zbl 0914.65132
Abramov, Sergei A.; Bronstein, Manuel; Petkovšek, Marko
25
1995
Indefinite sums of rational functions. Zbl 0914.65133
Abramov, S. A.
18
1995
Rational solutions of linear difference and \(q\)-differential equations with polynomial coefficients. Zbl 0910.65107
Abramov, S. A.
17
1995
Rational solutions of linear difference and \(q\)-difference equations with polynomial coefficients. Zbl 0914.65131
Abramov, S. A.
11
1995
D’Alembertian solutions to linear differential and difference equations. Zbl 0919.34013
Abramov, Sergei A.; Petkovšek, Marko
22
1994
The denominators of rational solutions to linear difference equations. Zbl 0824.33013
Abramov, S. A.
1
1994
On the greatest common divisor of polynomials which depend on a parameter. Zbl 0925.13009
Abramov, S. A.; Kvashenko, K. Yu.
3
1993
On d’Alembert substitution. Zbl 0921.34011
Abramov, S. A.
1
1993
Fast algorithms to search for the rational solutions of linear differential equations with polynomial coefficients. Zbl 0919.65045
Abramov, S. A.; Kvansenko, K. Yu.
6
1991
An algorithm for searching quasirational solutions of linear differential and difference equations with polynomial coefficients. Zbl 0727.65062
Abramov, S. A.
1
1991
Rational solutions of linear differential and difference equations with polynomial coefficients. Zbl 0719.65063
Abramov, S. A.
29
1989
Rational solutions of linear differential and difference equations with polynomial coefficients. Zbl 0695.65051
Abramov, S. A.
18
1989
Problems of computer algebra connected with the search for polynomial solutions of linear differential and difference equations. Zbl 0689.65049
Abramov, S. A.
7
1989
Problems of computer algebra involved in the search for polynomial solutions of linear differential and difference equations. Zbl 0723.65048
Abramov, S. A.
5
1989
The finite-difference second order equation with constant coefficients in the field of rational functions. Zbl 0369.39003
Abramov, S. A.
1
1977
The rational component of the solution of a first-order linear recurrence relation with a rational right side. Zbl 0352.65062
Abramov, S. A.
2
1976
Rationale Komponente der Lösung einer linearen rekurrenten Relation erster Ordnung mit rationaler rechter Seite. Zbl 0326.65069
Abramov, S. A.
16
1975
On the summation of rational functions. Zbl 0255.65003
Abramov, S. A.
8
1973
Über die Summation rationaler Funktionen. Zbl 0243.65076
Abramov, S. A.
12
1971
all top 5

Cited by 194 Authors

50 Abramov, Sergeĭ Aleksandrovich
23 Schneider, Carsten
17 Petkovšek, Marko
16 Khmelnov, Dennis E.
12 Barkatou, Moulay A.
11 Chen, Shaoshi
10 Kauers, Manuel
10 Ryabenko, Anna A.
7 Glück, Robert
7 Singer, Michael F.
7 van Hoeij, Mark
6 Blümlein, Johannes
6 Chen, William Yong-Chuan
6 Giesbrecht, Mark W.
6 Hou, Qinghu
6 Koutschan, Christoph
6 Mu, Yanping
5 Cluzeau, Thomas
5 Feng, Ruyong
5 Koepf, Wolfram A.
5 Panferov, Anton A.
4 Ablinger, Jakob
4 Bronstein, Manuel Eric
4 Gheffar, Amal
4 Labahn, George
4 Paramonov, Serge V.
4 Paule, Peter
4 Zima, Eugene V.
3 Axelsen, Holger Bock
3 Bogolyubskaya, A. A.
3 Bostan, Alin
3 Dreyfus, Thomas
3 Edneral, Victor F.
3 Garoufalidis, Stavros
3 Kotta, Ulle
3 Li, Ziming
3 Rostovtsev, Vitaly A.
3 Salvy, Bruno
3 Wang, Ronghua
3 Zeilberger, Doron
2 Chen, Vincent Y. B.
2 Cheng, Howard
2 Chyzak, Frédéric
2 Driver, Kathy A.
2 Foupouagnigni, Mama
2 Gao, Xiaoshan
2 Gu, Nancy Shan Shan
2 Halás, Miroslav
2 Hardouin, Charlotte
2 Huang, Hui
2 Kaarsgaard, Robin
2 Khavkine, Igor
2 Klein, Sebastian
2 Nishida, Naoki
2 Polyakov, S. P.
2 Prodinger, Helmut
2 Quadrat, Alban
2 Raab, Clemens G.
2 Saad, Husam L.
2 Sadykov, Timur Mradovich
2 Schost, Éric
2 Shishkina, Ol’ga Andreevna
2 Shkaravska, Olha
2 Sprenger, Torsten
2 Ulmer, Felix
2 van Eekelen, Marko
2 Vidal, Germán
2 Weideman, J. André C.
2 Weil, Jacques-Arthur
2 Yokoyama, Tetsuo
2 Zakrajšek, Helena
2 Zhang, Yi
1 Albert, Elvira
1 Alcazar, Juan Gerardo
1 Alekseeva, S. A.
1 Álvarez-Nodarse, Renato
1 Andrews, George Eyre
1 Apanovich, Marina Stepanovna
1 Arnold, John M.
1 Arreche, Carlos E.
1 Azzam, Jonas
1 Badouel, Eric
1 Baranov, M. I.
1 Bauer, Andrej
1 Beckermann, Bernhard
1 Belbachir, Hacene
1 Belikov, Juri
1 Biagioli, Riccardo
1 Böing, Harald
1 Bousquet-Mélou, Mireille
1 Brisebarre, Nicolas
1 Broughton, Gary
1 Cao, Jian
1 Carette, J. J.
1 Cattani, Eduardo H.
1 Cormier, Olivier
1 Cunha, Alcino
1 D’Andrea, Carlos
1 de Hon, Bastiaan P.
1 Dickenstein, Alicia M.
...and 94 more Authors
all top 5

Cited in 60 Serials

56 Journal of Symbolic Computation
39 Programming and Computer Software
16 Advances in Applied Mathematics
7 Computational Mathematics and Mathematical Physics
5 Applicable Algebra in Engineering, Communication and Computing
5 Journal of Difference Equations and Applications
4 Discrete Mathematics
4 Theoretical Computer Science
4 Journal of Systems Science and Complexity
4 Mathematics in Computer Science
4 ACM Communications in Computer Algebra
3 Journal of Mathematical Sciences (New York)
3 The Ramanujan Journal
2 Information Processing Letters
2 Mathematics of Computation
2 Journal of Algebra
2 Journal of Computational and Applied Mathematics
2 Mathematische Annalen
2 Annals of Combinatorics
2 Higher-Order and Symbolic Computation
2 Foundations of Computational Mathematics
1 International Journal of Modern Physics A
1 Acta Informatica
1 Computer Physics Communications
1 International Journal of Control
1 Journal of Mathematical Analysis and Applications
1 Journal of Mathematical Physics
1 Prikladnaya Matematika i Mekhanika
1 Annales de l’Institut Fourier
1 Applied Mathematics and Computation
1 Duke Mathematical Journal
1 Journal of Combinatorial Theory. Series A
1 Journal of Pure and Applied Algebra
1 Kybernetika
1 Quaestiones Mathematicae
1 Cybernetics
1 Computer Aided Geometric Design
1 Journal of Complexity
1 New Generation Computing
1 Differential Geometry and its Applications
1 Designs, Codes and Cryptography
1 Linear Algebra and its Applications
1 Journal of Knot Theory and its Ramifications
1 Nuclear Physics. B. Proceedings Supplements
1 The Electronic Journal of Combinatorics
1 Integral Transforms and Special Functions
1 Communications in Contemporary Mathematics
1 Algebraic & Geometric Topology
1 The Journal of Logic and Algebraic Programming
1 Journal of Algebra and its Applications
1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
1 Frontiers of Mathematics in China
1 Journal of Physics A: Mathematical and Theoretical
1 Logical Methods in Computer Science
1 Analysis & PDE
1 Proceedings of the Estonian Academy of Sciences
1 Izvestiya Irkutskogo Gosudarstvennogo Universiteta. Seriya Matematika
1 Axioms
1 Journal of Logical and Algebraic Methods in Programming
1 Journal of Siberian Federal University. Mathematics & Physics
all top 5

Cited in 40 Fields

117 Computer science (68-XX)
76 Special functions (33-XX)
51 Difference and functional equations (39-XX)
41 Field theory and polynomials (12-XX)
40 Ordinary differential equations (34-XX)
33 Numerical analysis (65-XX)
19 Combinatorics (05-XX)
15 Number theory (11-XX)
11 Commutative algebra (13-XX)
9 Quantum theory (81-XX)
7 Associative rings and algebras (16-XX)
6 Linear and multilinear algebra; matrix theory (15-XX)
6 Partial differential equations (35-XX)
5 Operator theory (47-XX)
4 Functions of a complex variable (30-XX)
4 Sequences, series, summability (40-XX)
4 Approximations and expansions (41-XX)
4 Systems theory; control (93-XX)
3 Manifolds and cell complexes (57-XX)
2 Mathematical logic and foundations (03-XX)
2 Algebraic geometry (14-XX)
2 Category theory; homological algebra (18-XX)
2 Group theory and generalizations (20-XX)
2 Information and communication theory, circuits (94-XX)
1 General and overarching topics; collections (00-XX)
1 History and biography (01-XX)
1 Order, lattices, ordered algebraic structures (06-XX)
1 Real functions (26-XX)
1 Potential theory (31-XX)
1 Several complex variables and analytic spaces (32-XX)
1 Harmonic analysis on Euclidean spaces (42-XX)
1 Integral transforms, operational calculus (44-XX)
1 Functional analysis (46-XX)
1 Calculus of variations and optimal control; optimization (49-XX)
1 Geometry (51-XX)
1 Convex and discrete geometry (52-XX)
1 Probability theory and stochastic processes (60-XX)
1 Mechanics of particles and systems (70-XX)
1 Statistical mechanics, structure of matter (82-XX)
1 Operations research, mathematical programming (90-XX)

Citations by Year

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