P-Adic Qth Roots Via Newton-Raphson Method

• Main Authors: Ignacio, Paul Samuel, Addawe, Joel, Nable, Job A
• Format: text
• Published: Archīum Ateneo 2016
• Subjects: p-adic number; Newton-Raphson; p-adic roots; Analysis; Mathematics
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/10; http://thaijmath.in.cmu.ac.th/index.php/thaijmath/article/view/937
• Institution: Ateneo De Manila University

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 r...