A pairwise independent random sampling method in the ring of $p$-adic integers

Abstract

Abstract For the ring ofp-adic integers,p being a fixed prime, any sequence which plays a similar role to Weyl’s irrational rotation has not been pro posed yet. We will see that a modifiedp-adic van der Corput sequence provides us with a reasonable c ounterpart of Weyl’s irrational rotation in the ring. We will pr esent a similar random Weyl sampling on the ring to the one proposed by Sugita and Tak anobu. In the process of establishing the counterpart, a sampling method bas ed on a function with naturally extended domain to the field of p-adic numbers in terms of the additive characters will be mentioned.