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


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.


Cusp Form Critical Line Laplace Eigenvalue Unique Ergodicity Maass Form 
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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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