Can I read Discrepancy of Arithmetic Progressions in Grids on EtoBox?

Discrepancy of Arithmetic Progressions in Grids by Fox, Jacob; Xu, Max Wenqiang; Zhou, Yunkun is a scholarly article available to read on EtoBox.

What is Discrepancy of Arithmetic Progressions in Grids about?

We prove that the the discrepancy of arithmetic progressions in the $d$-dimensional grid $\{1, \dots, N\}^d$ is within a constant factor depending only on $d$ of $N^{\frac{d}{2d+2}}$. This extends the case $d=1$, which is a celebrated result of Roth and of Matou\v{s}ek and Spencer, and removes the polylogarithmic factor from the previous upper bound of Valk\'o from about two decades ago. We further prove similarly tight bounds for grids of differing side lengths in many cases.

Author

Fox, Jacob; Xu, Max Wenqiang; Zhou, Yunkun

Published

2021

Language

EN