We prove lower bounds for the discrete negative -th moment of the derivative of the Riemann zeta function for all fractional . The bounds are in line with a conjecture of Gonek and Hejhal. Along the way, we prove a general formula for the discrete twisted second moment of the Riemann zeta function. This agrees with a conjecture of Conrey and Snaith.
Winston Heap. Junxian Li. Jing Zhao. "Lower bounds for discrete negative moments of the Riemann zeta function." Algebra Number Theory 16 (7) 1589 - 1625, 2022. https://doi.org/10.2140/ant.2022.16.1589