Mean values of L-functions and symmetry

  title={Mean values of L-functions and symmetry},
  author={J. Brian Conrey and David W. Farmer},
  journal={International Mathematics Research Notices},
  • J. Conrey, D. Farmer
  • Published 13 December 1999
  • Mathematics
  • International Mathematics Research Notices
Recently Katz and Sarnak introduced the idea of a symmetry group attached to a family of L-functions, and they gave strong evidence that the symmetry group governs many properties of the distribution of zeros of the L-functions. We consider the mean-values of the L-functions and the mollified mean-square of the L-functions and find evidence that these are also governed by the symmetry group. We use recent work of Keating and Snaith to give a complete description of these mean values. We find a… 
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