noun
Meaning 1
A p-adic absolute value, for a given prime number p, the function, denoted |..|p and defined on the rational numbers, such that |0|p = 0 and, for x≠0, |x|p = p^(-ordp(x)), where ordp(x) is the p-adic ordinal of x; the same function, extended to the p-adic numbers Qp (the completion of the rational numbers with respect to the p-adic ultrametric defined by said absolute value); the same function, further extended to some extension of Qp (for example, its algebraic closure).
Definition source: English Wiktionary via Wiktextract
Topics: mathematics, number-theory, sciences
Examples
- 2002, M. Ram Murty, Introduction to p-adic Analytic Number Theory, American Mathematical Society, page 114, By the property of the p'''-adic norm, (or by the “isosceles triangle principle”) we deduce that operatorname ordpa_r=rλ1.
- 2006, Matti Pitkanen, Topological Geometrodynamics, Luniver Press, page 531, The definition of p-adic norm should obey the usual conditions, in particular the requirement that the norm of product is product of norms.
Meaning relationships
Synonyms: none provided
Antonyms: none provided