The Wiener spectrum and Taylor series with pseudo-random coefficients
Mikhail Sodin
Tel Aviv University, Israel
https://scholar.google.com/citations?user=BFsA92YAAAAJ&hl=en
Date(s) : 07/10/2019 iCal
10h00 - 11h00
The theme of my talk will be the influence of the multipliers ξ(n) on the angular distribution of zeroes of the Taylor series 
This is a classical topic initiated by Littlewood together with his pupils and collaborators Chen, Nassif, and Offord. Our main finding is that the leading term in the asymptotic behaviour of log |Fξ(z)| (and hence, the distribution of zeroes of Fξ) is governed by the Wiener spectrum of the sequence ξ, that is, by the support of spectral measure of ξ. It applies to random stationary sequences, to the sequences ξ(n) = exp(nβ) with non-integer β > 1 and ξ(n) = exp(Q(n)), where Q is a Weyl polynomial, to Besicovitch almost periodic sequences, to multiplicative random sequences, and to the Möbius function (assuming “the binary Chowla conjecture”). The talk will be based on the joint works with Jacques Benatar, Alexander Borichev, and Alon Nishry (arXiv:1409.2736, 1908.09161).
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