Abstract:Hensel’s lemma has been the basis for the computation of the square roots of p-adic numbers in Zp. We generalize this problem to the computation of qth roots of p-adic numbers in Qp, where q is a prim...Hensel’s lemma has been the basis for the computation of the square roots of p-adic numbers in Zp. We generalize this problem to the computation of qth roots of p-adic numbers in Qp, where q is a prime and p is greater than q. We provide necessary and sufficient conditions for the existence of qth roots of p-adic numbers in Qp. Then, given a root of order r, we use the Newton-Raphson method to approximate the qth root of a p-adic number a. We also determine the rate of convergence of this method and the number of iterations needed for a specified number of correct digits in the approximate.Read More
Publication Year: 2015
Publication Date: 2015-02-24
Language: en
Type: article
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