Publication Date

2005

Journal or Book Title

Journal de théorie des nombres de Bordeaux

Abstract

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∈ℚ-ℤ <0 , Filaseta and Lam have shown that the nth degree Generalized Laguerre Polynomial L n (α) (x)=∑ j=0 n 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,±1 2,-1-n.

Comments

This is the pre-published version harvested from ArXiv. The published version is located at http://jtnb.cedram.org/item?id=JTNB_2005__17_2_517_0

http://archive.numdam.org/ARCHIVE/JTNB/JTNB_2005__17_2/JTNB_2005__17_2_517_0/JTNB_2005__17_2_517_0.pdf

Pages

517-525

Volume

17

Issue

2

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