Multiple exponential and character sums with monomials

We obtain new bounds of multivariate exponential sums with monomials, when the variables run over rather short intervals. Furthermore, we use the same method to derive estimates on similar sums with multiplicative characters to which previously known methods do not apply. In particular, in the case of multiplicative characters modulo a prime p¼ we break the barrier of p for ranges of individual variables.11 page(s