On the number of real roots of a solvable polynomial

C. U. Jensen

Displaying similar documents to “On the number of real roots of a solvable polynomial”

On Solvable Number Fields.

Jürgen Neukirch (1979)

Inventiones mathematicae

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New solvable cases of m-machine and n-element sequencing problems

J. Grabowski, M. M. Sysło (1975)

Applicationes Mathematicae

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On the Galois spectra of polynomials with integral parameters.

Sergeev, A.E., Yakovlev, A.V. (2005)

Zapiski Nauchnykh Seminarov POMI

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Corrigendum to the paper: "Linear relations between roots of polynomials" (Acta Arith. 89 (1999), 53-96)

Kurt Girstmair (2003)

Acta Arithmetica

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The Solvable Length of a Solvable Linear Group.

John D. Dixon (1968)

Mathematische Zeitschrift

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On the Galois group of generalized Laguerre polynomials

Farshid Hajir (2005)

Journal de Théorie des Nombres de Bordeaux

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Using the theory of Newton Polygons, we formulate a simple criterion for the Galois group of a polynomial to be “large.” For a fixed $α \in ℚ - ℤ_{< 0}$ , Filaseta and Lam have shown that the $n$ th degree Generalized Laguerre Polynomial $L_{n}^{(α)} (x) = \sum_{j = 0}^{n} (\binom{n + α}{n - j}) {(- x)}^{j} / j!$ is irreducible for all large enough $n$ . We use our criterion to show that, under these conditions, the Galois group of $L_{n}^{(α)} (x)$ is either the alternating or symmetric group on $n$ letters, generalizing results of Schur for $α = 0, 1, \pm \frac{1}{2}, - 1 - n$ .

Computation of the Galois group of a polynomial with rational coefficients.

Durov, N.V. (2004)

Zapiski Nauchnykh Seminarov POMI

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Computation of the Galois group of a polynomial with rational coefficients. II.

Durov, N.V. (2005)

Journal of Mathematical Sciences (New York)

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Differential Galois realization of double covers

Teresa Crespo, Zbigniew Hajto (2002)

Annales de l’institut Fourier

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An effective construction of homogeneous linear differential equations of order 2 with Galois group $2 A_{4}, 2 S_{4}$ or $2 A_{5}$ is presented.

Solvable-by-finite groups as differential Galois groups

Claude Mitschi, Michael F. Singer (2002)

Annales de la Faculté des sciences de Toulouse : Mathématiques

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