Power-free values of polynomials on symmetric varieties
نویسندگان
چکیده
منابع مشابه
Power-free Values of Polynomials on Symmetric Varieties
Given a symmetric variety Y defined over Q and a non-zero polynomial with integer coefficients, we use techniques from homogeneous dynamics to establish conditions under which the polynomial can be made r-free for a Zariski dense set of integral points on Y . We also establish an asymptotic counting formula for this set. In the special case that Y is a quadric hypersurface, we give explicit bou...
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For an irreducible polynomial in at most two variables the problem of representing power-free integers is investigated. Mathematics Subject Classification (2000). 11N32.
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Résumé. Soit f ∈ Z[x] un polynôme de degré r ≥ 3 sans racines de multiplicité r ou (r − 1). Supposons que f(x) 6≡ 0 mod p admette une solution dans (Z/p) pour tout p. Erdős a conjecturé que f(p) est donc sans facteurs puissances (r − 1)ièmes pour un nombre infini de premiers p. On prouve cela pour toutes les fonctions f dont une racine génère le corps de décomposition, et également pour d’autre...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2017
ISSN: 0024-6115
DOI: 10.1112/plms.12030