Uniform Distribution of g-Adic Integers

Uniform distribution of sequences of integers

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uniform distribution theory MULTIDIMENSIONAL EFFECTIVE S - ADIC SUBSHIFTS ARE SOFIC

In this article we prove that multidimensional effective S-adic systems, obtained by applying an effective sequence of substitutions chosen among a finite set of substitutions, are sofic subshifts. Communicated by Pierre Liardet

THE RING OF p-ADIC INTEGERS

Let k > 1 be an integer and let p be a prime. We show that if pa 6 k < 2pa or k = paq + 1 (with q < p/2) for some a = 1, 2, 3, . . . , then the set { (n k ) : n = 0, 1, 2, . . . } is dense in the ring Zp of p-adic integers, i.e., it contains a complete system of residues modulo any power of p.

Fibonacci Expansions and "f-adic" Integers

A Fibonacci expansion of a nonnegative integer n is an expression of n as a sum of Fibonacci numbers Fk with k > 2. It may be thought of as a partition of n into Fibonacci parts. The most commonly studied such expansion is the unique one in which the parts are all distinct and no two consecutive Fibonacci numbers appear. C. G. Lekkerkerker first showed this expansion was unique in 1952 [5]. The...

Group Rings over the p-Adic Integers