Digital expansions with respect to different bases (Q1396181)

The authors study the distribution and the average of the \(k\)th digit in the base \(g\)-expansion of \(N\), when \(g\) varies in the interval \([2,N']\). They also study the average of the sum of digits in the same framework. Their method consists of fine evaluations of exponential sums and ``\(\psi\)-sums'', where \(\psi\) is the first Bernoulli polynomial (i.e., \(\psi(x)= x-\lfloor x\rfloor- \frac 12\)).