P-adic Weierstrass Factor Theorem Through Newton Polygons

Abstract

Firstly, we will introduce some preliminary theory about Newton Polygons while presenting some comments for their uses. Our main focus is analyzing the Newton Polgons of general functions, specifically power series, of which a few important lemmas are shown. Finally, we collate our work into showing the Weierstrass Factor Theorem in the p-adic case.

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