Periodic Arithmetical Functions and Gauss Sums

Abstract

Let k be a positive integer. An arithmetical function f is said to be periodic with period k (or periodic modulo k) if

$$f\left( {n + k} \right) = f\left( n \right)$$

for all integers n. If k is a period so is mk for any integer m > 0. The smallest positive period of f is called the fundamental period.