On a discrete approach to lower bounds in discrepancy theory
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866912258998665216 |
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| author | Brandolini, Luca Gariboldi, Bianca Gigante, Giacomo Monguzzi, Alessandro |
| author_facet | Brandolini, Luca Gariboldi, Bianca Gigante, Giacomo Monguzzi, Alessandro |
| contents | In this paper, we prove that some renowned lower bounds in discrepancy theory admit a discrete analogue. Namely, we prove that the lower bound of the discrepancy for corners in the unit cube due to Roth holds true also for a suitable finite family of corners. We also prove two analogous results for the discrepancy on the torus with respect to squares and balls. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_10668 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On a discrete approach to lower bounds in discrepancy theory Brandolini, Luca Gariboldi, Bianca Gigante, Giacomo Monguzzi, Alessandro Classical Analysis and ODEs Number Theory 11K38, 39A12 In this paper, we prove that some renowned lower bounds in discrepancy theory admit a discrete analogue. Namely, we prove that the lower bound of the discrepancy for corners in the unit cube due to Roth holds true also for a suitable finite family of corners. We also prove two analogous results for the discrepancy on the torus with respect to squares and balls. |
| title | On a discrete approach to lower bounds in discrepancy theory |
| topic | Classical Analysis and ODEs Number Theory 11K38, 39A12 |
| url | https://arxiv.org/abs/2312.10668 |