  We first study the mean value of certain restricted divisor sums involving
the Chowla-Walum sums, improving in particular a recent estimate given by
Iannucci. The aim of the second part of this work is the generalization of the
previous study, by restricting the range of the divisors in the studied divisor
sums, extending the Chowla-Walum conjecture, proving a small part of this
extended conjecture and generalizing the asymptotic formulas previously
obtained in the first part.
