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arXiv · 1311.5726

On exponential sums over multiplicative subgroups of medium size

Ilya D. Shkredov
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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^{c_1}, p^{c_2}], where c_1,c_2 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.

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Ilya D. Shkredov. 2013-11-22. On exponential sums over multiplicative subgroups of medium size. https://arxiv.org/abs/1311.5726

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