P-Adic Qth Roots Via Newton-Raphson Method
Document Type
Article
Publication Date
2016
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 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.
Recommended Citation
Ignacio, Paul Samuel; Addawe, Joel; and Nable, Job A., (2016). P-Adic Qth Roots Via Newton-Raphson Method. Archīum.ATENEO.
https://archium.ateneo.edu/mathematics-faculty-pubs/10