Quantitative version of Beurling-Helson theorem

2014/01/17 by Konyagin, Sergei V., Shkredov, Ilya D.
#Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1401.4429

Abstract

It is proved that any continuous function f on the unit circle such that the sequence e^{in f}, n=1,2,... has small Wiener norm ‖ e^{in f} ‖_A = o (\fraclog^1/22 |n|(log log |n|)^3/11), is linear. Moreover, we get lower bounds for Wiener norm of characteristic functions of subsets from Z_p in the case of prime p.

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