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- W2194223804 abstract "We investigate necessary and sufficient conditions for an arbitrary polynomial of degree $n$ to be trivial, i.e. to have the form $a(z-b)^n$. These results are related to an open problem, conjectured in 2001 by E. Casas- Alvero. It says, that any complex univariate polynomial, having a common root with each of its non-constant derivative must be a power of a linear polynomial. In particular, we establish determinantal representation of the Abel-Goncharov interpolation polynomials, related to the problem and having its own interest. Among other results are new Sz.-Nagy type identities for complex roots and a generalization of the Schoenberg conjectured analog of Rolle's theorem for polynomials with real and complex coefficients." @default.
- W2194223804 created "2016-06-24" @default.
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- W2194223804 date "2015-04-01" @default.
- W2194223804 modified "2023-09-27" @default.
- W2194223804 title "Towards the Casas- Alvero conjecture" @default.
- W2194223804 hasPublicationYear "2015" @default.
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