Optimal Sine and Sawtooth Inequalities
| Autor: | Louis Esser, Terence Tao, Burt Totaro, Chengxi Wang |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
Mathematics - Algebraic Geometry
Mathematics::Combinatorics 42A05 (Primary) 11K06 26D05 (Secondary) Mathematics - Classical Analysis and ODEs Mathematics::Number Theory Applied Mathematics General Mathematics Classical Analysis and ODEs (math.CA) FOS: Mathematics Algebraic Geometry (math.AG) Analysis |
| Zdroj: | Journal of Fourier Analysis and Applications. 28 |
| ISSN: | 1531-5851 1069-5869 |
| DOI: | 10.1007/s00041-022-09909-7 |
| Popis: | We determine the optimal inequality of the form $\sum_{k=1}^m a_k\sin kx\leq 1$, in the sense that $\sum_{k=1}^m a_k$ is maximal. We also solve exactly the analogous problem for the sawtooth (or signed fractional part) function. Equivalently, we solve exactly an optimization problem about equidistribution on the unit circle. Comment: 19 pages, 6 figures; v2: Omitted the application to algebraic varieties of general type with small volume, in view of better results for that problem in arXiv:2109.13383 |
| Databáze: | OpenAIRE |
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