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Geometric & Functional Analysis GAFA

, Volume 12, Issue 6, pp 1296–1323 | Cite as

Subconvexity for Rankin-Selberg L-Functions of Maass Forms

  • Jianya Liu
  • Yangbo Ye
Original Paper

Abstract.

In this paper we prove a subconvexity bound for Rankin–Selberg L-functions \(L(s,f \otimes g)\) associated with a Maass cusp form f and a fixed cusp form g in the aspect of the Laplace eigenvalue 1/4 + k2 of f, on the critical line Re s = 1/2. Using this subconvexity bound, we prove the equidistribution conjecture of Rudnick and Sarnak [RS] on quantum unique ergodicity for dihedral Maass forms, following the work of Sarnak [S2] and Watson [W]. Also proved here is that the generalized Lindelöf hypothesis for the central value of our L-function is true on average.

Keywords

Cusp Form Critical Line Laplace Eigenvalue Unique Ergodicity Maass Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag, Basel 2002

Authors and Affiliations

  1. 1.Department of MathematicsShandong UniversityJinan, ShandongChina
  2. 2.Department of MathematicsThe University of IowaIowa CityUSA

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