Exponential sum estimates over a subgroup in an arbitrary finite field
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Let F q be the finite field consisting of q = p r elements and yy an additive character of the field F q . Take an arbitrary multiplicative subgroup H of size |H| > q C/(log log q) for some constant C > 0 not largely contained in any multiplicative shift of a subfield. We show that |Σ h∈H yy(h)| = o(|H|). This means that H is equidistributed in F q .
KeywordsArbitrary Element Prime Order Additive Character Arbitrary Subset Multiplicative Subgroup
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