Corpus ID: 214605699

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. 
1 Citations
Lower bound for higher moments of the mixed product of twisted L-functions
  • Guohua Chen, Xiaoguang He
  • 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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