Optimal Sine and Sawtooth Inequalities

Louis Esser, Terence Tao, Burt Totaro, Chengxi Wang

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 languageEnglish (US)
Article number14
JournalJournal of Fourier Analysis and Applications
Issue number2
StatePublished - Apr 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • General Mathematics
  • Applied Mathematics


  • Equidistribution
  • Sawtooth function
  • Sine inequality


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