p-adic

English

Etymology

From Template:Suffix. The letter Template:M follows common number theory usage in representing an arbitrary prime number; the suffix Template:M 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

1. Template:Lb Of, pertaining to, (ultimately) derived from or defined in the context of p-adic numbers.
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   • 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

     ${\mathbb{Z}}_p=\{x\in {\mathbb{Q}}_p:|x{|}_p\le 1\}$.

   • 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 $L^q$

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Usage notes

The synonym Template:M 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 Template:W.

Synonyms

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Translations

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See also

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Further reading

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