p-adic field

[‚pē ′ad·ik ¦fēld]

(mathematics)

For a fixed prime number, p, the set of all p-adic numbers, with addition and multiplication defined in a natural way.

References in periodicals archive ?

He does assume they have already seen some non-archimedean fields, usually the p-adic numbers and hopefully the complete algebraically closed p-adic field Cp, but he reviews them briefly just in case.

Dynamics in One Non-Archimedean Variable

Infinite extension of the p-adic field or the rational field, J.

On some Hasse principles for algebraic groups over global fields. II

Now, we can look for some applications to Hayman's problem in a p-adic field. Let f [member of] M (K).

Ojeda Hayman's Conjecture over a p-adic field. Taiwanese Journal of Mathematics.

Zeros of the derivative of a p-adic meromorphic function and applications

Let X = [V.sub.P], the valuation ring of the p-adic field [Q.sub.P].

Weighted composition maps and ideals

They illustrate the theory with many examples, including matrix groups with entries in the field of real or complex numbers, or other locally compact fields such as p-adic field, isometry groups of various metric spaces, and discrete groups themselves.

Metric Geometry of Locally Compact Groups

But the tools used in that study, such as properties of normal families, have no analogue on a p-adic field. Here we shall use other methods, particularly the non-Archimedean Nevanlinna Theory.

Value distribution of p-adic meromorphic functions

In fact they established stability of Cauchy functional equations over p-adic fields. In (17), (18) and (20) the stability of Cauchy, quadratic and quartic functional equations in non-Archimedean normed spaces were investigated.