On bilinear exponential and character sums with reciprocals of polynomials

We give non-trivial bounds for the bilinear sums [Equation presented here] where e_p(z) is a non-trivial additive character of the prime finite field F_p of p elements, with integers U,V, a polynomial ƒϵF_p[X] and some complex weights {α_u}, {β_v}. In particular, for ƒ(X)=aX+b, we obtain new bounds of bilinear sums with Kloosterman fractions. We also obtain new bounds for similar sums with multiplicative characters of F_p.