76 citations · 382 across the 37 of their papers we have counts for
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Reductive linear differential algebraic groups and the Galois groups of parameterized linear differential equations
Andrey Minchenko, Alexey Ovchinnikov, Michael F. Singer
We develop the representation theory for reductive linear differential algebraic groups (LDAGs). In particular, we exhibit an explicit sharp upper bound for orders of derivatives i…
Desingularization Explains Order-Degree Curves for Ore Operators
Shaoshi Chen, Maximilian Jaroschek, Manuel Kauers +1
Desingularization is the problem of finding a left multiple of a given Ore operator in which some factor of the leading coefficient of the original operator is removed. An order-de…
Unipotent differential algebraic groups as parameterized differential Galois groups
Andrey Minchenko, Alexey Ovchinnikov, Michael F. Singer
We deal with aspects of the direct and inverse problems in parameterized Picard-Vessiot (PPV) theory. It is known that, for certain fields, a linear differential algebraic group (L…