Sums with convolutions of Dirichlet characters to cube-free modulus

Abstract

We find estimates for short sums of the form Σnm≤X x1 (n)x 2 (m), where x1 and x2 are non-principal Dirichlet characters to modulus q, a cubefree integer, and X can be taken as small as q 1/2+j{cyrillic, ukrainian}. © 2011 American Mathematical Society.