Niklas Fraccaro

math.NT — Number Theory

A lower bound for the sixth moment of the Riemann zeta function

Contributed by Niklas Fraccaro

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 approximation by admissible profiles, gives the stated bound.