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- Publisher
- de Gruyter
- Copyright
- © 2020 Walter de Gruyter GmbH, Berlin/Boston
- ISSN
- 0933-7741
- eISSN
- 1435-5337
- DOI
- 10.1515/forum-2018-0292
- Publisher site
- See Article on Publisher Site
Abstract
AbstractWe establish explicit Ichino’s formulae for the central values of thetriple product L-functions with emphasis on the calculations for the real place.The key ingredient for our computations is Proposition 8which generalizes a result in [P. Michel and A. Venkatesh,The subconvexity problem for GL2{\rm GL}_{2},Publ. Math. Inst. Hautes Études Sci. 111 2010, 171–271].As an application we prove the optimal upper bound of a sum of restricted L2{L^{2}}-normsof the L2{L^{2}}-normalized newforms on certain quadratic extensions with prime level and boundedspectral parameter following the methods in [V. Blomer,On the 4-norm of an automorphic form,J. Eur. Math. Soc. (JEMS) 15 2013, 5, 1825–1852].
Journal
Forum Mathematicum – de Gruyter
Published: Jan 1, 2021