Type: Article

New estimates for exponential sums over multiplicative subgroups and intervals in prime field

Di Benedetto, D.; Garaev, M.Z.; García V. C.;

Abstract:

Let H be a multiplicative subgroup of Fp? of order H>p1/4. We show that max(a,p)=1?|?x?Hep(ax)|?H1?31/2880+o(1), where ep(z)=exp?(2?iz/p), which improves a result of Bourgain and Garaev (2009). We also obtain new estimates for double exponential sums with product nx with x?H and n?N for a short interval N of consecutive integers.