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amplification method

Journal of the Institute of Mathematics of Jussieu (1)

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EXTREME VALUES OF GEODESIC PERIODS ON ARITHMETIC HYPERBOLIC SURFACES
Part of
- Discontinuous groups and automorphic forms
Bart Michels
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 21 / Issue 5 / September 2022

Published online by Cambridge University Press:

22 December 2020, pp. 1507-1542

Print publication:

September 2022
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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.