On a Discrete Approach to Lower Bounds in Discrepancy Theory
Abstract 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.
Authors
- Luca Brandolini (ORCID: https://orcid.org/0000-0002-9670-9051)
- Bianca Gariboldi (ORCID: https://orcid.org/0000-0001-8714-4135)
- Giacomo Gigante (ORCID: https://orcid.org/0000-0002-1642-679X)
- Alessandro Monguzzi (ORCID: https://orcid.org/0000-0003-3233-5000)
Institutions
- University of Bergamo (IT)
Publication Details
- Journal
- Journal of Fourier Analysis and Applications
- Published
- 2025-03-11
- DOI
- https://doi.org/10.1007/s00041-025-10152-z
- Primary Topic
- Mathematical Approximation and Integration
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Università degli studi di Bergamo