On the orthogonal symmetry of L-functions of a family of Hecke Grössencharacters

@article{Conrey2012OnTO,
  title={On the orthogonal symmetry of L-functions of a family of Hecke Gr{\"o}ssencharacters},
  author={J. Brian Conrey and Nina C. Snaith},
  journal={Acta Arithmetica},
  year={2012},
  volume={157},
  pages={323-356}
}
The family of symmetric powers of an L-function associated with an elliptic curve with complex multiplication has received much attention from algebraic, automorphic and p-adic points of view. Here we examine this family from the perspectives of classical analytic number theory and random matrix theory, especially focusing on evidence for the symmetry type of the family. In particular, we investigate the values at the central point and give evidence that this family can be modeled by ensembles… 

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