EXTREME VALUES OF GEODESIC PERIODS ON ARITHMETIC HYPERBOLIC SURFACES

@article{Michels2020EXTREMEVO,
  title={EXTREME VALUES OF GEODESIC PERIODS ON ARITHMETIC HYPERBOLIC SURFACES},
  author={Bart Michels},
  journal={Journal of the Institute of Mathematics of Jussieu},
  year={2020},
  volume={21},
  pages={1507 - 1542}
}
  • Bart Michels
  • Published 12 February 2020
  • Mathematics
  • Journal of the Institute of Mathematics of Jussieu
Abstract Given a closed geodesic on a compact arithmetic hyperbolic surface, we show the existence of a sequence of Laplacian eigenfunctions whose integrals along the geodesic exhibit nontrivial growth. Via Waldspurger’s formula we deduce a lower bound for central values of Rankin-Selberg L-functions of Maass forms times theta series associated to real quadratic fields. 

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We prove a new omega result for toric periods of Hecke-Maass forms on compact locally symmetric spaces associated to forms of PGL3. This is motivated by conjectures on the maximal growth of

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