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math.CA2014★ 2 cited
On Wiener norm of subsets of Z_p of medium size
Sergei V. Konyagin, Ilya D. Shkredov
We give a lower bound for Wiener norm of characteristic function of subsets A from Z_p, p is a prime number, in the situation when exp((log p/log log p)^{1/3}) \le |A| \le p/3.
math.CA2014
Quantitative version of Beurling-Helson theorem
Sergei V. Konyagin, Ilya D. Shkredov
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 (\frac{\log^{1/22} |n|}{(\log \…