The main results are related to computer algebra (symbolic computation), linear ordinary differential and (q-)difference equations. Algorithms to solve the following problems were proposed: the decomposition of indefinite sums of rational functions (an analogue of integral algorithms by Hermite and Ostrogradskii); the same problem for indefinite sums of hypergeometric terms (with M. Petkovsek); constructing rational solutions of linear differential and (q-)difference equations with polynomial coefficients; the same problem for systems of equations (with M. Barkatou and M. Bronstein); constructing q-hypergeometric solutions of linear q-difference equations with polynomial coefficients (with M. Petkovsek and P. Paule). In the context of the theory of non-commutative Ore polynomials a number of algorithms were designed (these algorithms are adjustable for differential, difference, q-difference and some other cases): an algorithm for "accurate integration" of solutions of equations (with M. van Hoeij); an algorithm for the peripheral factorization of Ore polynomials (with S. P. Tsarev); an algorithm to search for d'Alembertian solutions (with M. Petkovsek for the homogeneous case, with E. V. Zima for equations with d'Alembertian right-hand sides). Some algorithms, related to power series solutions were proposed: given a linear ordinary differential equation with polynomial coefficients, to find the points where the equation has power series solution with hypergeometric coefficients (with M. Petkovsek and A. A. Ryabenko); to find the points where the equation has power series solution with sparse sequence of coefficients, etc. A correct algorithmical solution of the orbit problem for algebraic numbers (with M. Bronstein). The well-known Zeilberger's algorithm, which is a useful tool to prove combinatorial identities, was improved. First, the problem of recognizing if Zeilberger's algorithm is applicable to a given hypergeometric term (i.e., the algorithm terminates in finite time) was solved. Second, a method to reduce the complexity of the item-by-item examination inherent in Zeilberger's algorithm was proposed (with H. Q. Le). The Wilf–Zeilberger conjecture that a hypergeometric term is proper iff it is holonomic was proven (with M. Petkovsek). Outside of symbolic computation, e.g., the "multiple cards algorithm" to control the questions of a learning system (with G. G. Gnezdilova) and the optimal-in-average algorithm to search for the maximal and the minimal elements of finite set of numbers were proposed.

Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1969 (department of topology). Ph.D. thesis was defended in 1972. D.Sci. thesis was defended in 1983. A list of my works contains more than 100 titles. Since 1992 I and E. V. Zima, A. P. Kryukov, V. A. Rostovtsev have led the research seminar at MSU on symbolic computation (computer algebra).

• Abramov S., Petkovsek M., Ryabenko A. Special formal series solutions of linear operator equations // Discrete Math., 2000, 210, 3–25.
• Abramov S., van Hoeij M. Integration of solutions of linear functional equations // Integral transforms and special functions, 1999, V. 8, no. 1–2, 3–12.
• Abramov S. m-Sparse solutions of linear ordinary differential equations with polynomial coefficients // Discrete Math., 2000, 217, 3–15.
• Abramov S., Bronstein M. On solutions of linear functional systems // Proceedings of ISSAC'01, 2001, London, ACM Press, 1–6.

• Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow
• University of Waterloo
• Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
• Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow
• Computing Centre, USSR Academy of Sciences