Title: The Wiener spectrum and Taylor series with pseudo-random coefficients.
Abstract:
The theme of my talk will be the influence of the arguments of the coefficients of Taylor series with infinite radius of convergence on their zero distribution. This is a classical topic initiated by Littlewood together with his pupils and collaborators Chen, Nassif, and Offord, which still remains a terra incognita within the complex analysis. Our main finding, is that the asymptotic zero distribution is governed by pair correlations, more precisely, by the Wiener spectrum. This allows us to treat many new instances of pseudo-random sequences (among them are stationary ergodic sequences, Besicovitch
almost-periodic sequences, the Mobius function (modulo the Chowla conjecture) and its random counterparts), as well as practically all known ones.
The talk will be based on the joint works with Jacques Benatar, Alexander Borichev, and Alon Nishry
(arXiv:1409.2736, 1908.09161)