On exponential sums over multiplicative subgroups of medium size

2013/11/22 by Shkredov, Ilya D.
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1311.5726

Abstract

In the paper we obtain some new upper bounds for exponential sums over multiplicative subgroups G of F^*_p having sizes in the range [p^c₁, p^c₂], where c₁,c₂ are some absolute constants close to 1/2. As an application we prove that in symmetric case G is always an additive basis of order five, provided by |G| > p^1/2 log^1/3 p. Also the method allows us to give a new upper bound for Heilbronn's exponential sum.

Related

• Exponential sums over small subgroups, revisited
• Incomplete exponential sums over exponential functions
• Intersections of multiplicative subgroups and Heilbronn's exponential sum
• New estimates for exponential sums over multiplicative subgroups and\n intervals in prime fields
• Bounds on exponential sums over small multiplicative subgroups