Digit Variance and Dedekind Sums Original Research Article

Letpgreater-or-equal, slanted3 be a prime number,bgreater-or-equal, slanted2 a primitive root mod pandzan integer, 1less-than-or-equals, slantzless-than-or-equals, slantp−1. The digit expansion ofz/pwith respect to the basisbhas a period consisting of the firstp−1 digitsc1, …, cp−1. We express the varianceσ2ofc1, …, cp−1in terms of the Dedekind sums(p, b) and investigate the behaviour ofσ2forbfixed andp→∞. The reciprocity law for Dedekind sums is the most important tool in this investigation.