For the Riemann zeta-function we consider the fourth moment whose square part admits a shift along the real line. Asymptotic formulas are obtained for the shift parameter around 0 and for the one in unbounded regions.
"Fourth Moment of the Riemann Zeta-function with a Shift along the Real Line." Tokyo J. Math. 36 (2) 355 - 377, December 2013. https://doi.org/10.3836/tjm/1391177976