# A new bound K2/3+ɛ for Rankin-Selberg ℒ-functions for Hecke congruence subgroups

@inproceedings{Lau2010ANB,
title={A new bound K2/3+ɛ for Rankin-Selberg ℒ-functions for Hecke congruence subgroups},
author={Yuk-kam. Lau and Jianya Liu and Yangbo Ye},
year={2010}
}
• Published 8 July 2010
• Mathematics
Let f be a holomorphic Hecke eigenform for Γ0(N ) of weight k, or a Maass eigenform for Γ0(N ) with Laplace eigenvalue 1/4 + k. Let g be a fixed holomorphic or Maass cusp form for Γ0(N ). A subconvexity bound for central values of the Rankin-Selberg L-function L(s, f ⊗ g) is proved in the k-aspect: L(1/2+ it, f ⊗ g) N ,g,t,e k, while a convexity bound is only k. This new bound improves earlier subconvexity bounds for these Rankin-Selberg L-functions by Sarnak, the authors, and Blomer…
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## References

SHOWING 1-10 OF 32 REFERENCES
The fourth power moment of automorphic $L$-functions for $GL(2)$ over a short interval
In this paper we will prove bounds for the fourth power moment in the t aspect over a short interval of automorphic L-functions L(s, g) for GL(2) on the central critical line Re s = 1/2. Here g is a
Subconvexity for Rankin-Selberg L-Functions of Maass Forms
• Mathematics
• 2002
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
Rankin-Selberg L-functions on the critical line
Let f and g be two primitive (holomorphic or Maass) cusp forms of arbitrary level, character and infinity parameter by which we mean the weight in the holomorphic case and the spectral parameter in
Holomorphic extensions of representations: (I) automorphic functions
• Mathematics
• 2002
Let G be a connected, real, semisimple Lie group contained in its complexification GC, and let K be a maximal compact subgroup of G. We construct a KC-G double coset domain in GC, and we show that
Uniform bound for HeckeL-functions
• Mathematics
• 2005
Our principal aim in the present article is to establish a uniform hybrid bound for individual values on the critical line of Hecke $L$-functions associated with cusp forms over the full modular
On sums of Hecke series in short intervals
On a Σ K-G≤K+G α j H j 3 (1/2) << GK 1+e pour K e ≤G≤K, ou α j =|ρ j (1)| 2 (cosh πκ j ) -1 est le premier coefficient de Fourier de forme de Maass correspondant a la valeur propre λ j =κ 2 j + 1/4 a
Analytic continuation of representations and estimates of automorphic forms
• Mathematics
• 1999
0.1. Analytic vectors and their analytic continuation. Let G be a Lie group and (�,G,V ) a continuous representation of G in a topological vector space V. A vector v ∈ V is called analytic if the
• Mathematics
• 2006
The subconvexity problem for Rankin–Selberg L-functions and equidistribution of Heegner points. II
• Mathematics
• 2005
We prove a general subconvex bound in the level aspect for Rankin–Selberg L-functions associated with two primitive holomorphic or Maass cusp forms over Q. We use this bound to establish the