The Fourth Power Moment of Automorphic L-functions for Gl(2) over a Short Interval
نویسندگان
چکیده
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 fixed holomorphic or Maass Hecke eigenform for the modular group SL2(Z), or in certain cases, for the Hecke congruence subgroup Γ0(N ) with N > 1. The short interval is from a large K to K + K103/135+ε. The proof is based on an estimate in the proof of subconvexity bounds for Rankin-Selberg L-function for Maass forms by Jianya Liu and Yangbo Ye (2002) and Yuk-Kam Lau, Jianya Liu, and Yangbo Ye (2004), which in turn relies on the Kuznetsov formula (1981) and bounds for shifted convolution sums of Fourier coefficients of a cusp form proved by Sarnak (2001) and by Lau, Liu, and Ye (2004).
منابع مشابه
Mollification of the fourth moment of automorphic L-functions and arithmetic applications
In this paper, we compute the twisted fourth power moment of modular L-functions of prime level near the critical line. This allows us to prove some new non-vanishing results on the central values of automorphic L-functions, in particular whose obtained by base change from GL2(Q) to GL2(K) for K a cyclic field of low degree.
متن کاملOn the analytic properties of intertwining operators I: global normalizing factors
We provide a uniform estimate for the $L^1$-norm (over any interval of bounded length) of the logarithmic derivatives of global normalizing factors associated to intertwining operators for the following reductive groups over number fields: inner forms of $operatorname{GL}(n)$; quasi-split classical groups and their similitude groups; the exceptional group $G_2$. This estimate is a key in...
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 کاملThe 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 کامل