The Galois group of generic symmetric matrices

Cohen, Stephen D.

Displaying similar documents to “The Galois group of generic symmetric matrices”

Note on a problem of Chowla

B. Birch, H Swinnerton-Dyer (1959)

Acta Arithmetica

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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.

Polynomials whose Galois groups are Frobenius groups with prime order complement

Leonardo Cangelmi (1994)

Journal de théorie des nombres de Bordeaux

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We give an effective characterization theorem for integral monic irreducible polynomials $f$ of degree $n$ whose Galois groups over $ℚ$ are Frobenius groups with kernel of order $n$ and complement of prime order.

On the Galois groups of cubics and trinomials

Phyllis Lefton (1979)

Acta Arithmetica

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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 $α = 0, 1, \pm \frac{1}{2}, - 1 - n$ .

Matrix powers over finite fields.

Acosta-de-Orozco, Maria T., Gomez-Calderon, Javier (1992)

International Journal of Mathematics and Mathematical Sciences

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Polynomials of Galois representations attached to elliptic curves.

A. Reverter, N. Vila (2000)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

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