Some Notes on Flat Polynomials

2014/02/22 by El Houcein El Abdalaoui, Abdalaoui, e. H. el, Mahendra Nadkarni +1 · 2 citations
Mathematics · #30C10 #37A05 #37A40 #42A55 #Analytic Number Theory Research #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematical functions and polynomials #Primary 42A05 #Secondary 37A30 #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.1402.5457

openalex publication_date 2014/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Connection of flat polynomials with some spectral questions in ergodic theory is discussed. A necessary condition for a sequence of polynomials of the type (1)/(√(N)) (1 +∑_j=1^N-1 z^n_j) to be flat in almost everywhere sense is given, which contrasts with a similar necessary condition for a sequence of polynomials to be ultraflat.

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• A generalization of Littlewood's L^α flat theorem, α>0
• On flat polynomials with non-Negative coefficients

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