In number theory, given a prime number p, the p-adic numbers form an extension of the rational numbers which is distinct from the real numbers, though...

In number theory, the p-adic valuation or p-adic order of an integer n is the exponent of the highest power of the prime number p that divides n. It is...

In mathematics, p-adic analysis is a branch of number theory that studies functions of p-adic numbers. Along with the more classical fields of real and...

In mathematics, particularly p-adic analysis, the p-adic exponential function is a p-adic analogue of the usual exponential function on the complex numbers...

target are p-adic (where p is a prime number). For example, the domain could be the p-adic integers Zp, a profinite p-group, or a p-adic family of Galois...

d p ) {\displaystyle (\mathbb {Q} ,d_{p})} ⁠ is not complete, and its completion is the p-adic number field ⁠ Q p . {\displaystyle \mathbb {Q} _{p}.}...

In mathematics, p-adic Teichmüller theory describes the "uniformization" of p-adic curves and their moduli, generalizing the usual Teichmüller theory that...

{\displaystyle \mathbb {Q} } lead to the fields Q p {\displaystyle \mathbb {Q} _{p}} of p-adic numbers (for any prime number p), which are thereby analogous to R {\displaystyle...

dynamics Algebraic function field Arithmetic topology Finite field p-adic number List of number theoretic algorithms The term 'arithmetic' may have regained...

mathematics, a p-adic distribution is an analogue of ordinary distributions (i.e. generalized functions) that takes values in a ring of p-adic numbers. If...

matrix-valued geometric series, function-valued geometric series, p {\displaystyle p} -adic number geometric series, and most generally geometric series of elements...

integers, they can also take other forms in different contexts (such as P-adic number). Googology delves into the naming conventions and properties of these...

In mathematics, p-adic Hodge theory is a theory that provides a way to classify and study p-adic Galois representations of characteristic 0 local fields...

In mathematics, the p-adic gamma function Γp is a function of a p-adic variable analogous to the gamma function. It was first explicitly defined by Morita...

In mathematics, a p-adic modular form is a p-adic analog of a modular form, with coefficients that are p-adic numbers rather than complex numbers. Serre...

concept in social psychology Triadic relation, a mathematical concept p-adic number, where p=3, a mathematical concept Triadic System in Psychiatry Tertian This...

Lazard's solution to Hilbert's fifth problem over the p-adic numbers, shows that a pro-p group is p-adic analytic if and only if it has finite rank, i.e. there...

Arithmetic dynamics Kaprekar number p-adic number p-adic analysis Zero-divisor See Gérard Michon's article at "spherical number". Oxford English Dictionary...

Assistant director in charge adic may refer to: adicity of an operation the I-adic filtration, I-adic completion, or I-adic topology of a ring or module...

function fields, algebraic number fields, and p-adic fields are commonly used and studied in mathematics, particularly in number theory and algebraic geometry...

In mathematics, a p-adically closed field is a field that enjoys a closure property that is a close analogue for p-adic fields to what real closure is...

identity, meaning that any number multiplied by 1 equals the same number. 1 is by convention not considered a prime number. In digital technology, 1 represents...

many other meanings. In logic and philosophy, arity may also be called adicity and degree. In linguistics, it is usually named valency. In general, functions...

or Mordell–Tornheim zeta function of several variables p-adic zeta function of a p-adic number Prime zeta function, like the Riemann zeta function, but...

automorphism Chebotarev's density theorem Totally real field Local field p-adic number p-adic analysis Adele ring Idele group Idele class group Adelic algebraic...

give the fields of p-adic numbers, where p {\displaystyle p} is a prime integer number (see below); since the p {\displaystyle p} -adic absolute values satisfy...

rational number or even all rational numbers can often be established by verifying that the result holds true for each of the p-adic number systems. There...

rational number is a square of a rational number if it is a square of a p-adic number for almost all prime numbers p. It was introduced by Wilhelm Grunwald (1933)...

{\displaystyle p} ⁠-adic absolute value | q | p {\displaystyle |q|_{p}} of any rational number ⁠ q {\displaystyle q} ⁠ is then defined as ⁠ | q | p = p − ν p ( q...

matrix-valued geometric series, function-valued geometric series, p {\displaystyle p} -adic number geometric series, and most generally geometric series of elements...