New Digit Results and Several Problems

0≤n<x:n≡l( mod m) (−1)g In the case q = 2 we write Sm,l,2 = Sm,l, σ2(n) = σ(n). We call (2) a generalized Newman sum. In [7] we gave a quite another proof of the Coquet’s estimates for S3,0(x) and a fast algorithm for its calculation. Professor J.-P.Allouche kindly informed me about a misprint in Coquet’s theorem: for odd x η = η(x) = (−1) (but (−1) as in [2]; sf. [1], pp.98-99) An important role in our proof belongs to the formula: for an even n