2017/02/15 by Jacob Carruth, Carruth, Jacob, Noam Elkies +5
Mathematics · #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Graph theory and applications #Limits and Structures in Graph Theory #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1702.04579
openalex publication_date 2017/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we investigate a high dimensional version of Selberg's minorant problem for the indicator function of an interval. In particular, we study the corresponding problem of minorizing the indicator function of the box QN=[-1,1]N by a function whose Fourier transform is supported in the same box QN. We show that when the dimension is sufficiently large there are no minorants with positive mass and we give an explicit lower bound for such dimension. On the other hand, we explicitly construct minorants for dimensions 1,2,3,4 and 5 and, as an application, we use them to produce an improved diophantine inequality for exponential sums.