Mikhail Sodin, Tel Aviv:Zeroes of random and pseudorandom Taylor series

We will discuss the influence of the arguments of the coefficients of Taylor series on the angular distribution of zeroes of the entire function represented by this series. This problem goes back to the works of Littlewood and his pupils and collaborators Offord, Nassif, Chen.

We suggest a new aproach to this problem. First, using some potential theory, we reduce the question to lower bounds of certain exponential sums of Weyl's type. Such lower bounds, in turn, depend on the spectrum of a certain autocorrelation function. We show how this method works in several basic examples of arithmetic and of ergodic nature, which apparently were unavailable by the previous techniques.

This is a joint work in progress with Alexander Borichev and Alon Nishry.

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