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math.NT2024
Lower bounds for shifted moments of the Riemann zeta function
Michael J. Curran
In previous work, the author gave upper bounds for the shifted moments of the zeta function \[ M_{α,β}(T) = \int_T^{2T} \prod_{k = 1}^m |ζ(\tfrac{1}{2} + i (t + α_k))|^{2 β_k} dt \…
math.NT2024
Sharp bounds for joint moments of the Riemann zeta function
Michael J. Curran, André Heycock
In previous work, the first author obtained conjecturally sharp upper bounds for the joint moments of the power of the Riemann zeta function with the $2h^{\te…
math.NT2023
Correlations of the Riemann zeta function
Michael J. Curran
Assuming the Riemann hypothesis, we investigate the shifted moments of the zeta function \[ M_{α,β}(T) = \int_T^{2T} \prod_{k = 1}^m |ζ(\tfrac{1}{2} + i (t + α_k))|^{2 β_k} dt \] i…