V2EX p-adic

P-adic

定义(中文) / Definition

p-adic(p进的):指以某个素数 p 为基础建立的一套“度量/数系”与相关概念(如 p-adic 数p-adic 范数/赋值p-adic 分析)。它用“能被 p 的高次幂整除得越多,就越接近”的方式来衡量大小与距离,常用于数论与代数。

发音(IPA) / Pronunciation

/pi dk/

例句 / Examples

P-adic numbers are used in number theory.
p-adic 数在数论中被广泛使用。

The argument uses a p-adic valuation to compare how closely two integers agree modulo powers of p.
这个论证使用 p-adic 赋值来比较两个整数在模 p 的幂意义下“吻合得有多接近”。

词源(中文) / Etymology

p-adic 来自字母 p(通常表示一个素数)与后缀化的 -adic(表示“与某种进制/度量体系相关”)。这一术语与 Kurt Hensel(亨泽尔)在 19 世纪末提出的 p-adische Zahlen(p-adic numbers)相关,用来描述以素数 p 为核心构造的数系与分析方法。

相关词汇 / Related Word

文学与名著中的用例 / Notable Works

  • p-adic Numbers: An Introduction(Fernando Q. Gouvêa)
  • p-adic Numbers, p-adic Analysis, and Zeta-Functions(Neal Koblitz)
  • A Course in Arithmetic(Jean-Pierre Serre)
  • Local Fields(Jean-Pierre Serre)
  • Algebraic Number Theory(Jürgen Neukirch)
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