Limit Theorems for a class of unbounded observables on the real line with an application to sampling the Lindelöf Hypothesis

by Dr Kasun Fernando (Centro De Giorgi - SNS)

Wednesday 7 Dec 2022, 15:00 → 16:00 Europe/Rome

Centro De Giorgi - SNS

 We prove the Central Limit Theorem, first order Edgeworth expansion and Mixing Local Limit Theorem for the Birkhoff sums of a class of L^3 observables over Boolean-type transformations on the real line. The class of observables include the real part, the imaginary part and the absolute value of Riemann zeta function. This result is in the spirit of a result by Steuding who has proven a strong law of large numbers for "sampling the Lindelöf Hypothesis". This is join work with Tanja Schindler (University of Vienna).