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Published June 14, 2018 | Submitted
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Large deviations in Selberg's central limit theorem


Following Selberg it is known that as T → ∞, [formula] uniformly for Δ ≤ (log log log T)^((1/2) - ε). We extend the range of Δ to Δ « (log log T)^((1/10) - ε). We also speculate on the size of the largest Δ for which the above normal approximation can hold and on the correct approximation beyond this point.

Additional Information

The author is partially supported by a NSERC PGS-D award.

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August 19, 2023
October 18, 2023