English

Optimal sine and sawtooth inequalities

Algebraic Geometry 2021-09-30 v2 Classical Analysis and ODEs

Abstract

We determine the optimal inequality of the form k=1maksinkx1\sum_{k=1}^m a_k\sin kx\leq 1, in the sense that k=1mak\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.

Keywords

Cite

@article{arxiv.2107.11058,
  title  = {Optimal sine and sawtooth inequalities},
  author = {Louis Esser and Terence Tao and Burt Totaro and Chengxi Wang},
  journal= {arXiv preprint arXiv:2107.11058},
  year   = {2021}
}

Comments

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

R2 v1 2026-06-24T04:27:11.787Z