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