Student Probability and Mathematical Physics Seminar

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Statistical Properties of the Riemann Zeta Function

Speaker: Yuchen Fan, CIMS

Location: Warren Weaver Hall 201

Date: Tuesday, February 3, 2026, 12:30 p.m.

Synopsis:

The Riemann Zeta Function is a central object in mathematics. Despite the Riemann Hypothesis, which asserts that the zeros of the zeta function are located on the 1/2 critical line, its other statistical properties are also very interesting to study and bridge connections between number theory and other fields of mathematics, such as probability theory. Such properties include (but are not limited to) the Bohr-Jessen theorem, Selberg’s Central limit theorem, the statistics of zeros at different scales, rigidity, their correlations (Montgomery Conjecture, CUE hypothesis), its moments (Keating-Snaith Conjecture), its extreme values (Lindelöf Hypothesis) and local fluctuations (FHK, Saksman-Webb, etc.).