Higher uniformity of arithmetic functions in short intervals I. All intervals

Kaisa Matomäki, Xuancheng Shao, Terence Tao +1

We study higher uniformity properties of the Möbius function $\mu$, the von Mangoldt function $\Lambda$, and the divisor functions $d_k$ on short intervals $(X,X+H]$ with $X^{θ+\varepsilon…