Galois groups over rational function fields and Explicit Hilbert Irreducibility

نویسندگان

چکیده

Let P∈Q[t,x] be a polynomial in two variables with rational coefficients, and let G the Galois group of P over field Q(t). It follows from Hilbert's Irreducibility Theorem that for most numbers c specialized P(c,x) has isomorphic to factors same way as P. In this paper we discuss methods computing obtaining an explicit description exceptional c, i.e., those which different or differently To illustrate determine specializations three sample polynomials. addition, apply our techniques prove new result arithmetic dynamics.

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ژورنال

عنوان ژورنال: Journal of Symbolic Computation

سال: 2021

ISSN: ['1095-855X', '0747-7171']

DOI: https://doi.org/10.1016/j.jsc.2019.11.003