Optimal sine and sawtooth inequalities

2021/07/23 by Esser, Louis, Tao, Terence, Totaro, Burt +1
#26D05 (Secondary) #42A05 (Primary) 11K06 #Algebraic Geometry (math.AG) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.11058

Abstract

We determine the optimal inequality of the form ∑_k=1^m a_ksin kx≤ 1, in the sense that ∑_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.

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