Digit variance and Dedekind sums

[摘要] Let p greater than or equal to 3 be a prime number, b greater than or equal to 2 a primitive root mod p and z an integer, 1 less than or equal to z less than or equal to p-1. The digit expansion of z/p with respect to the basis b has a period consisting of the first p-1 digits c(1), ..., c(p-1). We express the variance sigma(2) of (c(1), ..., c(p-1) in terms of the Dedekind sum s(p, b) and investigate the behaviour of sigma(2) for b fixed and p --> infinity. The reciprocity law for Dedekind sums is the most important tool in this investigation. (C) 1997 Academic Press.

[发布日期] 1997-08-01