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Exponential sums of the M\"{o}bius function and flat polynomials

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arxiv 1910.10569 v3 pith:OWGVFDST submitted 2019-10-23 math.NT math.DS

el Houcein el Abdalaoui This is my paper · ORCID
classification math.NTmath.DS
keywords polynomialsproblemflatanalyticaskedbiuscasecoefficients
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abstract

We present an elementary problem on analytic polynomials with coefficients $\pm 1$ or in $\{0,\pm 1 \}$ which implies Riemann hypothesis. It is turns out that this problem is a particular case of the weak form of a flat polynomials problem asked by Erd\"os in his 1957's paper. We provide also under an extra-condition the converse.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$

    math.NT 2025-09 reject novelty 7.0 of 10

    Claims to confirm the L^α-Littlewood, L^1-Newman, and L^∞-Erdős conjectures via a short Clarkson-inequality argument, but the key norm-convergence step is unjustified.

  2. Local Moments of M\"obius Fourier Polynomials and the Riemann Hypothesis

    math.PR 2026-07 accept novelty 6.0 of 10

    RH is equivalent to subpolynomial growth of arbitrarily high finite local moments of normalized Möbius polynomials on arcs of radius c/N.

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