Skolem Density Problems over Large Galois Extensions of Global Fields
نویسندگان
چکیده
Let K be a global eld, V an innnite proper subset of the set of all primes of K, and S a nite subset of V. Denote the maximal Galois extension of K in which each p 2 S totally splits by K tot;S. Let M be an algebraic extension of K. A data for an (S; V)-Skolem density problem for M consists of a nite subset T of V containing S, polynomials f 1 ; : : : ; f m 2 ~ KX 1 ; : : : ; X n ] satisfying jf i j q = 1 for each non-archimedean prime q 2 ~ V r ~ T , a point a 2 M n , and a positive real number. A solution to the problem is a point x 2 M n such that jx i ? a i j p < for each p 2 ~ T and jx i j q 1, jf j (x)j q = 1 for each non-archimedean prime q 2 ~
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