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Pré-Publication, Document De Travail Année : 2015

Some Notes on Flat Polynomials

Mahendra G. M. G. Nadkarni
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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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Dates et versions

hal-01178322 , version 1 (18-07-2015)

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  • HAL Id : hal-01178322 , version 1

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El Houcein El Abdalaoui, Mahendra G. M. G. Nadkarni. Some Notes on Flat Polynomials. 2015. ⟨hal-01178322⟩
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