An effective Deligne's equidistribution theorem

Lei Fu; Ping Xi; Yuk-Kam Lau

An effective Deligne's equidistribution theorem

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arxiv 2406.09633 v2 pith:G75HDMOG submitted 2024-06-13 math.NT

Lei Fu , Yuk-Kam Lau , Ping Xi This is my paper · ORCID

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keywords deligneeffectiveequidistributiontheoremcompactdeducegroupsinequality

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We prove an Erd\H{o}s--Tur\'an type inequality for compact Lie groups, from which we deduce an effective version of Deligne's equidistribution theorem.

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Wasserstein metrics and quantitative equidistribution of exponential sums over finite fields
math.NT 2025-05 accept novelty 8.0 of 10

Explicit Wasserstein-distance rates are proved for equidistribution of ultra-short exponential sums and of Deligne-Katz trace-function families over finite fields.

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