<span class="searchmatch">p</span>-<span class="searchmatch">adic</span> <span class="searchmatch">ultrametric</span> (plural <span class="searchmatch">p</span>-<span class="searchmatch">adic</span> <span class="searchmatch">ultrametrics</span>) (number theory) The <span class="searchmatch">ultrametric</span> with prime number <span class="searchmatch">p</span> as parameter defined as d <span class="searchmatch">p</span> ( x , y ) = | x − y |...
to a <span class="searchmatch">p</span>-<span class="searchmatch">adic</span> <span class="searchmatch">ultrametric</span>. The expansion (21)2121p is equal to the rational <span class="searchmatch">p</span>-<span class="searchmatch">adic</span> number 2 <span class="searchmatch">p</span> + 1 <span class="searchmatch">p</span> 2 − 1 . {\displaystyle \textstyle {2p+1 \over <span class="searchmatch">p</span>^{2}-1}...
numbers): ℓ-<span class="searchmatch">adic</span> <span class="searchmatch">p</span>-<span class="searchmatch">adic</span> absolute value <span class="searchmatch">p</span>-<span class="searchmatch">adic</span> norm <span class="searchmatch">p</span>-<span class="searchmatch">adic</span> number <span class="searchmatch">p</span>-<span class="searchmatch">adic</span> order <span class="searchmatch">p</span>-<span class="searchmatch">adic</span> ordinal <span class="searchmatch">p</span>-<span class="searchmatch">adic</span> <span class="searchmatch">ultrametric</span> Translations ℓ-<span class="searchmatch">adic</span> cohomology <span class="searchmatch">p</span>-<span class="searchmatch">adic</span> Riemann...
numbers ℚp (the completion of the rational numbers with respect to the <span class="searchmatch">p</span>-<span class="searchmatch">adic</span> <span class="searchmatch">ultrametric</span> defined by said absolute value); the same function, further extended...
<span class="searchmatch">p</span>-<span class="searchmatch">adic</span> norm norm <span class="searchmatch">p</span>-<span class="searchmatch">adic</span> order, <span class="searchmatch">p</span>-<span class="searchmatch">adic</span> valuation <span class="searchmatch">p</span>-<span class="searchmatch">adic</span> <span class="searchmatch">ultrametric</span> ^ 2008, Jacqui Ramagge, Unreal Numbers: The story of <span class="searchmatch">p</span>-<span class="searchmatch">adic</span> numbers (PDF file) <span class="searchmatch">p</span>-adic...
to the infimum of a set of <span class="searchmatch">ultrametrics</span> because, in general, the infimum of a set of <span class="searchmatch">ultrametrics</span> is not necessarily an <span class="searchmatch">ultrametric</span>. <span class="searchmatch">p</span>-<span class="searchmatch">adic</span> <span class="searchmatch">ultrametric</span>...
derivative of a <span class="searchmatch">p</span>-<span class="searchmatch">adic</span> meromorphic function”, in Khodr Shamseddine, editor, Advances in <span class="searchmatch">Ultrametric</span> Analysis: 12th International Conference on <span class="searchmatch">p</span>-<span class="searchmatch">adic</span> Functional...