On Bilinear Exponential and Character Sums With Reciprocals of Polynomials

Abstract

Abstract. We give nontrivial bounds for the bilinear sumswhere e p (z) is a nontrivial additive character of the prime finite field F p of p elements, with integers U , V , a polynomial f ∈ F p [X] and some complex weights {α u } , {β v } . In particular, for f (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 .

Cancellations amongst Kloosterman sums

“…It is also natural to consider cancellations between some other exponential and character sums. For example, in [14] one can find some bound on the following sums…”