Arithmetic progressions in multiplicative groups of finite fields

Mei-Chu Chang

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arXiv · 1608.05449

Arithmetic progressions in multiplicative groups of finite fields

Mei-Chu Chang

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Abstract

Let $G$ be a multiplicative subgroup of the prime field $\mathbb F_p$ of size $|G|> p^{1-\kappa}$ and $r$ an arbitrarily fixed positive integer. Assuming $\kappa=\kappa(r)>0$ and $p$ large enough, it is shown that any proportional subset $A\subset G$ contains non-trivial arithmetic progressions of length $r$. The main ingredient is the Szemer\'{e}di-Green-Tao theorem.

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Mei-Chu Chang. 2016-08-18. Arithmetic progressions in multiplicative groups of finite fields. https://arxiv.org/abs/1608.05449

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