Some Notes on Flat Polynomials
Résumé
Connection of flat polynomials with some spectral questions in ergodic theory is discussed. A necessary condition for a sequence of polynomials of the type $\frac{1}{\sqrt{N}} \big(1 +\sum_{j=1}^{N-1} z^{n_j}\big)$
to be flat in almost everywhere sense is given, which contrasts with a similar necessary condition for a sequence of polynomials to be ultraflat. This connects the problem of existence of flat sequence (in. a.e. sense) of such polynomials with some problems in combinatorial number theory. This is a revised version of the earlier paper with the same title.
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