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Lower bounds for discrete negative moments of the Riemann zeta function

### Winston Heap, Junxian Li and Jing Zhao

Vol. 16 (2022), No. 7, 1589–1625
##### Abstract

We prove lower bounds for the discrete negative $2k$-th moment of the derivative of the Riemann zeta function for all fractional $k$. 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.

##### Keywords
Riemann zeta-function, twisted discrete moment, Gonek's conjecture
##### Mathematical Subject Classification
Primary: 11M06, 11N99