Fast arithmetic in unramified p-adic fields

Let p be prime and Zpn a degree n unramified extension of the ring of p-adic integers Zp. In this paper we give an overview of some very fast deterministic algorithms for common operations in Zpn modulo pN . Combining existing methods with recent work of Kedlaya and Umans about modular composition of polynomials, we achieve quasi-linear time algorithms in the parameters n and N, and quasi-linear or quasi-quadratic time in log p, for most basic operations on these fields, including Galois conjugation, Teichm

• Type: Journal
• Year: 2010
• Where: FFA
• Authors: Hendrik Hubrechts
• Keywords: Education, FFA 2010, P-adic Integers, Quasi-linear Time Algorithms, Zpn Modulo PN