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New results on Rademacher Fourier and Taylor series

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Mathematics and Physics of Anderson localization: 50 Years After

This is a report on a joint work in progress with Fedor Nazarov and Alon Nishry. We prove that any power of the logarithm of Rademacher Fourier series (i.e. a square summable Fourier series with random independent signs) is integrable. This result has several applications to zeroes and value-distribution of random Talor series. One of this applications gives asymptotics for the counting function of zeroes of arbitrary Taylor series with random independent signs, and proves their angular equidistribution. Another application answers an old question by J.-P.Kahane.

This talk is part of the Isaac Newton Institute Seminar Series series.

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