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arXiv · 1608.05448

Nonlinear Roth type theorems in finite fields

Jean Bourgain·Mei-Chu Chang
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Abstract

We obtain smoothing estimates for certain nonlinear convolution operators on prime fields, leading to quantitative nonlinear Roth type theorems. Compared with the usual linear setting (i.e. arithmetic progressions), the nonlinear nature of the operators leads to different phenomena, both qualitatively and quantitatively.

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Jean Bourgain, Mei-Chu Chang. 2016-08-18. Nonlinear Roth type theorems in finite fields. https://arxiv.org/abs/1608.05448

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