Applications of the L‐functions ratios conjectures

@article{Conrey2005ApplicationsOT,
  title={Applications of the L‐functions ratios conjectures},
  author={J. Brian Conrey and Nina C. Snaith},
  journal={Proceedings of the London Mathematical Society},
  year={2005},
  volume={94}
}
  • J. Conrey, N. Snaith
  • Published 21 September 2005
  • Mathematics
  • Proceedings of the London Mathematical Society
In upcoming papers by Conrey, Farmer and Zirnbauer there appear conjectural formulas for averages, over a family, of ratios of products of shifted L‐functions. In this paper we will present various applications of these ratios conjectures to a wide variety of problems that are of interest in number theory, such as lower order terms in the zero statistics of L‐functions, mollified moments of L‐functions and discrete averages over zeros of the Riemann zeta function. In particular, using the… 
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