论文标题
$ \ mathbb {f} _q^{\ infty} $的三项算术进展
Three-term arithmetic progressions in subsets of $\mathbb{F}_q^{\infty}$ of large Fourier dimension
论文作者
论文摘要
我们表明，$ \ mathbb {f} _q^{\ infty} $的子集必须包含三个期算术进度。这与福尔里尺寸$ 1 $的$ \ mathbb {r}子集的shmerkin的构造形成对比，没有三项算术进度。
We show that subsets of $\mathbb{F}_q^{\infty}$ of large Fourier dimension must contain three-term arithmetic progressions. This contrasts with a construction of Shmerkin of a subset of $\mathbb{R}$ of Fourier dimension $1$ with no three-term arithmetic progressions.
