New estimates for exponential sums over multiplicative subgroups and\n intervals in prime fields

2020/03/13 by Daniel Di Benedetto, Moubariz Z. Garaev, di Benedetto, Daniel +9
Social Sciences · #11T23 #FOS: Mathematics #Global Educational Reforms and Inequalities #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2003.06165

openalex publication_date 2020/03/13 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

Let mathcal H be a multiplicative subgroup of mathbbF_p^* of order\nH>p^1/4. We show that
max_(a,p)=1
left|
sum_x
in
mathcal H\n
mathbf
,e_p(ax)
right|
le H^{1-31/2880+o(1)}, where\n e_p(z) = \exp(2 \π i z/p), which improves a result of Bourgain\nand Garaev (2009). We also obtain new estimates for double exponential sums\nwith product nx with x \∈ mathcal H and n \∈ mathcal N for a\nshort interval mathcal N of consecutive integers.\n

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