English

Noun

p-adic ordinal ‎(plural p-adic ordinals)

1. (number theory) A function of rational numbers, with prime number p as parameter, which is defined for some non-zero integer x as the largest integer r such that p^r divides x; is defined for some non-zero rational number a/b as the p-adic ordinal of a minus the p-adic ordinal of b; and is defined for 0 as infinity. ^[1]

   Notice the resemblance between the p-adic ordinal and the base-p logarithm.

Usage notes

• The p-adic ordinal of rational number x can be denoted as .

Related terms

• p-adic norm

References

1. ↑ 2011, Andrew Baker, An Introduction to p-adic Numbers and p-adic Analysis, Definition 2.3