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- Title
On the jth smallest modulus of a covering system with distinct moduli.
- Authors
Klein, Jonah; Koukoulopoulos, Dimitris; Lemieux, Simon
- Abstract
Covering systems were introduced by Erdős in 1950. In the same article where he introduced them, he asked if the minimum modulus of a covering system with distinct moduli is bounded. In 2015, Hough answered affirmatively this long standing question. In 2022, Balister et al. gave a simpler and more versatile proof of Hough's result. Building upon their work, we show that there exists some absolute constant c > 0 such that the j th smallest modulus of a minimal covering system with distinct moduli is ≤ exp (c j 2 / log (j + 1)).
- Subjects
HOUGH transforms
- Publication
International Journal of Number Theory, 2024, Vol 20, Issue 2, p471
- ISSN
1793-0421
- Publication type
Article
- DOI
10.1142/S1793042124500234