Seminar
The zero distribution of Taylor series and the Wiener spectrum
by Jacques Benatar (Tel Aviv University)
Location: 200B.02.18, Leuven
Time: Tuesday April 14, 2020 at
14:00
In this talk we will explore the connection between the zero distribution of a given Taylor series (with infinite radius of convergence) and its coefficients. This classical topic initiated by Littlewood and his students/collaborators Chen, Nassif, and Offord, is still not well understood. A very broad but intriguing question is the following: “Under which conditions will the zeroes of a given Taylor series equidistribute in sectors ?” Our main finding is that the Wiener spectrum associated to the coefficients plays a crucial role. This idea allows us to treat new instances of pseudo-random sequences (including stationary ergodic sequences, Besicovitch almost-periodic sequences, the Mobius function (modulo the Chowla conjecture) and its random counterparts). This is joint work with Alexander Borichev and Mikhail Sodin (https://arxiv.org/abs/1908.09161).
