On the distribution of the residues of small multiplicative subgroups of $$
\mathbb{F}_p
$$ |
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Authors: | J Bourgain |
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Institution: | (1) School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA |
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Abstract: | Distributional properties of small multiplicative subgroups of are obtained. In particular, it is shown that if H < is of size larger than polylogarithmic in p, then, letting β < 1 be a fixed exponent, most elements of any coset aH (a ∈ , arbitrary) will not fall into the interval −p
β, p
β] ∈ . The arguments are based on the theory of heights and results from additive combinatoric. |
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Keywords: | |
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