The Second Moment of Gl(3)×gl(2) L-functions, Integrated
نویسنده
چکیده
We consider the family of Rankin-Selberg convolution L-functions of a fixed SL(3,Z) Maass form with the family of Hecke-Maass cusp forms on SL(2,Z). We estimate the second moment of this family of L-functions with a “long” integration in t-aspect. These L-functions are distinguished by their high degree (12) and large conductors (of size T ).
منابع مشابه
The Second Moment of Gl(3)×gl(2) L-functions at Special Points
For a fixed SL(3,Z) Maass form φ, we consider the family of L-functions L(φ× uj, s) where uj runs over the family of Hecke-Maass cusp forms on SL(2,Z). We obtain an estimate for the second moment of this family of L-functions at the special points 1 2 + itj consistent with the Lindelöf Hypothesis. We also obtain a similar upper bound on the sixth moment of the family of Hecke-Maass cusp forms a...
متن کامل2 00 4 Moments of L - functions , periods of cusp forms , and cancellation in additively twisted sums on GL ( n ) Stephen
In a previous paper with Schmid ([29]) we considered the regularity of automorphic distributions for GL(2,R), and its connections to other topics in number theory and analysis. In this paper we turn to the higher rank setting, establishing the nontrivial bound ∑ n≤T an e 2π i nα = Oε(T 3/4+ε), uniformly in α ∈ R, for an the coefficients of the L-function of a cusp form on GL(3,Z)\GL(3,R). We al...
متن کاملJ ul 2 00 4 Moments of L - functions , periods of cusp forms , and cancellation in additively twisted sums on GL ( n )
In a previous paper with Schmid [29] we considered the regularity of automorphic distributions for GL(2,R), and its connections to other topics in number theory and analysis. In this paper we turn to the higher rank setting, establishing the nontrivial bound ∑ n≤T an e 2π i nα = Oε(T 3/4+ε), uniformly in α ∈ R, for an the coefficients of the L-function of a cusp form on GL(3,Z)\GL(3,R). We also...
متن کاملA ug 2 00 4 Cancellation in additively twisted sums on GL ( n ) Stephen
In a previous paper with Schmid [29] we considered the regularity of automorphic distributions for GL(2,R), and its connections to other topics in number theory and analysis. In this paper we turn to the higher rank setting, establishing the nontrivial bound ∑ n≤T an e 2π i nα = Oε(T 3/4+ε), uniformly in α ∈ R, for an the coefficients of the L-function of a cusp form on GL(3,Z)\GL(3,R). We also...
متن کاملBounds for GL ( 3 ) × GL ( 2 ) L - functions and GL ( 3 ) L - functions
In this paper, we will give the subconvexity bounds for self-dual GL(3) L-functions in the t aspect as well as subconvexity bounds for self-dual GL(3) × GL(2) L-functions in the GL(2) spectral aspect.
متن کامل