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p-adic

From Wiktionary, the free dictionary

English

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Etymology

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From p +‎ -adic. The letter p follows common number theory usage in representing an arbitrary prime number; the suffix -adic signals that properties of the number p (generally, those due to its being prime, and specifically those of a specified p) are fundamental to the theory and determine the properties of the resulting construction.

Adjective

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p-adic (not comparable)

  1. (number theory) Of, pertaining to, (ultimately) derived from or defined in the context of p-adic numbers.
    • 1995, Alain Escassut, Analytic Elements in P-adic Analysis, World Scientific, page v:
      The theory of p-adic analytic functions in domains other than simple disks is not very well known yet, although such kind of functions happens to intervene in questions linked to p-adic functional analysis, number theory, and others.
    • 1997, Fernando Q. Gouvêa, p-adic Numbers: An Introduction, Springer, 2nd Edition, page 60,
      Definition 3.3.3 The ring of p-adic integers is the valuation ring
      .
    • 2007, Nguyen Minh Cheung, Nguyen Van Co, Le Quang Thuan, §12: Harmonic Analysis Over P-adic Field I: Some Equations and Singular Field Operators, N. M. Chuong, Yu V. Egorov, A. Khrennikov, Y. Meyer, D. Mumford (editors), Harmonic, Wavelet and P-adic Analysis, World Scientific, page 272,
      The paper is organized as follows:
      2. Preliminaries
      3. A p-adic Cauchy problem
      4. The p-adic Hilbert transform
      5. The boundaries in the p-adic space
      []

Usage notes

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The synonym ℓ-adic is used in some contexts: for instance, in regard to Galois representations (G-modules, where the Galois group G is a vector space over the field of ℓ-adic numbers), and in algebraic geometry, where ℓ-adic cohomology is one of the "classical" constructions of Weil cohomologies.

Synonyms

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Derived terms

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Translations

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See also

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Further reading

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