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Moments of the Riemann zeta function on the critical line: moment_isEquiv

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Statement

The asymptotic behaviour of the kkth moment of the Riemann zeta function is conjectured to be

1T∫0T∣ζ(1/2+it)∣2kdt∼cklog⁡(T)k2, \frac{1}{T}\int_0^T |\zeta(1/2 + it)|^{2k}dt \sim c_k \log(T)^{k^2},

for some constant ckc_k.

Lean statement

theorem moment_isEquiv (k : ℕ) : ∃ c > (0 : ℝ),
    moment k ~[atTop] fun T ↦ c * T.log ^ (k ^ 2) := by
  sorry

Sources(1)

Openness evidence

Tagged category research open in google-deepmind/formal-conjectures at commit a64e959c32c2. Definitions used by the statement are in FormalConjectures/Paper/RiemannZetaMoments.lean.

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