The p-adic norm is a mathematical term used to describe a way of measuring the size or magnitude of a number in a particular mathematical setting. It is sometimes referred to as the p-adic absolute value or p-adic valuation, and can also be called the non-Archimedean absolute value or the ultrametric distance function. The p-adic norm is often used in number theory and algebraic geometry to understand the behavior of number systems, and is related to the theory of modular forms and elliptic curves. Other terms that are sometimes used as synonyms for the p-adic norm include the p-adic metric, the p-adic distance, and the p-adic topology.