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math.CO2021
Discrepancy of arithmetic progressions in grids
Jacob Fox, Max Wenqiang Xu, Yunkun Zhou
We prove that the the discrepancy of arithmetic progressions in the -dimensional grid is within a constant factor depending only on of $N^{\frac{d}{2d+2}…
math.CO2021
Discrepancy in modular arithmetic progressions
Jacob Fox, Max Wenqiang Xu, Yunkun Zhou
Celebrated theorems of Roth and of Matoušek and Spencer together show that the discrepancy of arithmetic progressions in the first positive integers is . We study t…