An Effective Weierstrass Division Theorem
نویسنده
چکیده
We prove an effective Weierstrass Division Theorem for algebraic restricted power series with p-adic coefficients. The complexity of such power series is measured using a certain height function on the algebraic closure of the field of rational functions over Q. The paper includes a construction of this height function, following an idea of Kani. We apply the effective Weierstrass Division Theorem to obtain a number-theoretic criterion for membership in ideals of polynomial rings with integer coefficients.
منابع مشابه
Effective power series computations ∗
Let K be an effective field of characteristic zero. An effective tribe is a subset of K[[z1, z2, ...]] =K ∪K[[z1]] ∪K[[z1, z2]] ∪ ··· which is effectively stable under the Kalgebra operations, restricted division, composition, the implicit function theorem, as well as restricted monomial transformations with arbitrary rational exponents. Given an effective tribe with an effective zero test, we ...
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