Note on a problem of Chowla

B. Birch; H Swinnerton-Dyer

Displaying similar documents to “Note on a problem of Chowla”

Double transitivity of Galois groups of trinomials

S. D. Cohen, A. Movahhedi, A. Salinier (1997)

Acta Arithmetica

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The distribution of polynomials over finite fields

Stephen Cohen (1970)

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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.

The Galois group of generic symmetric matrices

Cohen, Stephen D. (1990)

Portugaliae mathematica

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

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.

Finiteness results for Hilbert's irreducibility theorem

Peter Müller (2002)

Annales de l’institut Fourier

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Let $k$ be a number field, $𝒪_{k}$ its ring of integers, and $f (t, X) \in k (t) [X]$ be an irreducible polynomial. Hilbert’s irreducibility theorem gives infinitely many integral specializations $t \mapsto \bar{t} \in 𝒪_{k}$ such that $f (\bar{t}, X)$ is still irreducible. In this paper we study the set ${Red}_{f} (𝒪_{k})$ of those $\bar{t} \in 𝒪_{k}$ with $f (\bar{t}, X)$ reducible. We show that ${Red}_{f} (𝒪_{k})$ is a finite set under rather weak assumptions. In particular, previous results obtained by diophantine approximation techniques, appear as special cases of some of our results. Our method is different. We use elementary...