Binomial exponential sums (2018)
AuthorsShparlinski IE, Voloch JFshow all
We obtain new bounds of exponential sums modulo a prime p with binomials axk + bxn. In particular, for k=1, we improve the bound of Karatsuba (1967) from O(n1/4 p3/4) to O(p3/4 + n1/3 p2/3) for any n, and then use it to improve the bound of Akulinichev (1965) from (p5/6) to O(p4/5) for n|(p-1). The result is based on a new bound on the number of solutions and of degrees of irreducible components of certain equations over finite fields.
ANZSRC Fields of Research01 - Mathematical Sciences::0101 - Pure Mathematics::010101 - Algebra and Number Theory
01 - Mathematical Sciences::0101 - Pure Mathematics::010102 - Algebraic and Differential Geometry