Optimal sine and sawtooth inequalities
Algebraic Geometry
2021-09-30 v2 Classical Analysis and ODEs
Abstract
We determine the optimal inequality of the form , in the sense that 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.
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