Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hilbert transforms and the equidistribution of zeros of polynomials   We improve the current bounds for an inequality of Erd\H{o}s and Tur\'an from
1950 related to the discrepancy of angular equidistribution of the zeros of a
given polynomial. Building upon a recent work of Soundararajan, we establish a
novel connection between this inequality and an extremal problem in Fourier
analysis involving the maxima of Hilbert transforms, for which we provide a
complete solution. Prior to Soundararajan (2019), refinements of the
discrepancy inequality of Erd\H{o}s and Tur\'an had been obtained by Ganelius
(1954) and Mignotte (1992).

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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int