Algebraic properties of a family of Jacobi polynomials
نویسندگان
چکیده
The one-parameter family of polynomials Jn(x, y) = ∑n j=0 ( y+j j ) x is a subfamily of the two-parameter family of Jacobi polynomials. We prove that for each n ≥ 6, the polynomial Jn(x, y0) is irreducible over Q for all but finitely many y0 ∈ Q. If n is odd, then with the exception of a finite set of y0, the Galois group of Jn(x, y0) is Sn; if n is even, then the exceptional set is thin.
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