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Stanislav Molchanov : On the random analytic functions

The talk will contain a review of several recent results on the analytic continuation of the random analytic functions. We will start from the classical theorem on the random Taylor series (going to Borel’ s school), but the main subject will be the random zeta – function (which was introduced implicitly by Cramer) and its generalizations. We will show that “true primes are not truly random “, since zeta – functions for the random “pseudo-primes” (in the spirit of Cramer) have no analytic continuation through the critical line Re (z) = 1/2.

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