On multiplicative energy of subsets of varieties

2021/01/24 by Shkredov, Ilya D. · 2 citations
#Algebraic Geometry (math.AG) #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2101.09770

Abstract

We obtain a non--trivial upper bound for the multiplicative energy of any sufficiently large subset of a subvariety of a finite algebraic group. We also find some applications of our results to growth of conjugates classes, estimates of exponential sums and the restriction phenomenon.

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