Optimal Sine and Sawtooth Inequalities

Louis Esser; Terence Tao; Burt Totaro; Chengxi Wang

doi:10.1007/s00041-022-09909-7

Optimal Sine and Sawtooth Inequalities

Louis Esser, Terence Tao, Burt Totaro, Chengxi Wang

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We determine the optimal inequality of the form ∑k=1maksinkx≤1, in the sense that ∑k=1mak 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.

Original language	English (US)
Article number	14
Journal	Journal of Fourier Analysis and Applications
Volume	28
Issue number	2
DOIs	https://doi.org/10.1007/s00041-022-09909-7
State	Published - Apr 2022
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
General Mathematics
Applied Mathematics

Keywords

Equidistribution
Sawtooth function
Sine inequality

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10.1007/s00041-022-09909-7

Cite this

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abstract = "We determine the optimal inequality of the form ∑k=1maksinkx≤1, in the sense that ∑k=1mak 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.",

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author = "Louis Esser and Terence Tao and Burt Totaro and Chengxi Wang",

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AU - Esser, Louis

AU - Tao, Terence

AU - Totaro, Burt

AU - Wang, Chengxi

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N2 - We determine the optimal inequality of the form ∑k=1maksinkx≤1, in the sense that ∑k=1mak 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.

AB - We determine the optimal inequality of the form ∑k=1maksinkx≤1, in the sense that ∑k=1mak 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.

KW - Equidistribution

KW - Sawtooth function

KW - Sine inequality

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ER -

Optimal Sine and Sawtooth Inequalities

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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