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arXiv · 1904.04457

Hausdorff dimension of the large values of Weyl sums

Changhao Chen·Igor E. Shparlinski
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Abstract

The authors have recently obtained a lower bound of the Hausdorff dimension of the sets of vectors $(x_1, \ldots, x_d)\in [0,1)^d$ with large Weyl sums, namely of vectors for which $$ \left| \sum_{n=1}^{N}\exp(2\pi i (x_1 n+\ldots +x_d n^{d})) \right| \ge N^{\alpha} $$ for infinitely many integers $N \ge 1$. Here we obtain an upper bound for the Hausdorff dimension of these exceptional sets.

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Changhao Chen, Igor E. Shparlinski. 2019-04-09. Hausdorff dimension of the large values of Weyl sums. https://arxiv.org/abs/1904.04457

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