Zeros of Moment Generating Functions and the Riemann Hypothesis
Talkat Deterministic Counting, Probability, and Zeros of Partition Functions (Simons Institute workshop, 2019) · 2019-03-18..03-22
summary
Defines the Riemann hypothesis as the statement that the Laplace transform of a specific even positive rapidly decaying Phi has all zeros on the imaginary axis, and isolates a critical de Bruijn–Newman constant Λ so that the pure-imaginary-zeros property holds for all real λ ≥ Λ and fails for λ < Λ. Key tools are the backwards heat equation governing zero motion and a pair-correlation/spacings analysis of zeros; de Bruijn gives Λ ≤ 1/2, a 1976 result gives Λ > −∞, recent Rodgers–Tao work proves Λ ≥ 0, so RH is equivalent to Λ = 0.
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