# Lower bounds for discrete negative moments of the Riemann zeta function

@article{Heap2020LowerBF, title={Lower bounds for discrete negative moments of the Riemann zeta function}, author={Winston Heap and Junxian Li and Jing Zhao}, journal={arXiv: Number Theory}, year={2020} }

We prove lower bounds for the discrete negative $2k$th moment of the derivative of the Riemann zeta function for all fractional $k\geqslant 0$. 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.

#### One Citation

Lower bound for higher moments of the mixed product of twisted L-functions

- Mathematics
- 2021

Abstract Let f 1 , f 2 be two fixed distinct holomorphic cuspidal Hecke eigenforms of level 1 and respective weights κ 1 , κ 2 with κ 1 ≡ κ 2 ( mod 4 ) . Let L ( s , f 1 ⊗ χ ) , L ( s , f 2 ⊗ χ )… Expand

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