A lower bound for the sixth moment of the Riemann zeta function
We prove that the lower limit of the sixth moment of the Riemann zeta function, normalized by $(a_3/9!)T(\log T)^9$, is greater than $41.007$. Our approach extends the two-piece amplifier construction used by Durkan and Page by allowing independent profiles, centered derivatives, and finite real linear combinations of two projected test families. An asymmetric twisted fourth-moment estimate and their amplified moment formula yield a common numerator kernel. Explicit balanced and unbalanced kernels determine the projected Gram form. A rational certificate with 250 tests, followed by…
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