Type: Article
Publication Date: 2001-01-01
Citations: 27
DOI: https://doi.org/10.1023/a:1011803816545
We estimate some sums of the shape S(Xβ1,…, Xβm): = [sum ] 1 [les ] d1 [les ] Xβ1… [sum ]1 [les ] dm [les ] Xβmƒ(d1,…, dm), when m ∈ and f is a nonnegative arithmetical function. We relate them to the behaviour of the associated Dirichlet seriesF(s1,…, sm) = ∞[sum ]d1 = 1 … ∞[sum ]dm = 1f(d1,…, dm)/d1s1 … dmsm. The main aim of this work is to develop analytic tools to count the rational points of bounded height on toric varieties.