13 Citations
Simultaneous non-vanishing of GL(3) × GL(2) and GL(2) L-functions
- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 2011
Abstract Fix g a Hecke–Maass form for SL3(). In the family of holomorphic newforms f of fixed weight and large prime level q, we find the average value of the product $L(\half,g\times f)L(\half,f)$.…
Non-vanishing of derivatives of (3)×(2) -functions
- Mathematics
- 2012
Let f be a fixed self-dual Hecke-Maass cusp form for SL3(Z) and let Bk be an orthogonal basis of holomorphic cusp forms of weight k ≡ 2(mod 4) for SL2(Z). We prove an asymptotic formula for the first…
The 8th Moment of the Family of $\Gamma_1(q)$-Automorphic $L$-Functions
- MathematicsInternational Mathematics Research Notices
- 2018
We prove a Lindel\"of on average bound for the eighth moment of a family of $L$-functions attached to automorphic forms on $GL(2)$, the first time this has been accomplished. Previously, such a bound…
A hybrid asymptotic formula for the second moment of Rankin–Selberg L‐functions
- Mathematics
- 2012
Let g be a fixed modular form of full level, and let {fj, k} be a basis of holomorphic cuspidal newforms of even weight k, fixed level and fixed primitive nebentypus. We consider the Rankin–Selberg…
Moments for L-functions for GLr×GLr-1
- Mathematics
- 2012
We establish a spectral identity for moments of Rankin–Selberg L-functions on GL r ×GL r − 1 over arbitrary number fields, generalizing our previous results for r = 2.
Rankin–Selberg periods for spherical principal series
- Mathematicsmanuscripta mathematica
- 2021
By the unfolding method, Rankin-Selberg L-functions for ${\rm GL}(n)\times{\rm GL}(m)$ can be expressed in terms of period integrals. These period integrals actually define invariant forms on tensor…
The second moment of $$GL(3) \times GL(2) L$$-functions at special points
- Mathematics
- 2009
For a fixed $$SL(3,\mathbb Z )$$ Maass form $$\phi $$, we consider the family of $$L$$-functions $$L(\phi \times u_j, s)$$ where $$u_j$$ runs over the family of Hecke-Maass cusp forms on…
The L2 restriction norm of a GL3 Maass form
- MathematicsCompositio Mathematica
- 2012
Abstract We prove a sharp upper bound on the L2 norm of a GL3 Maass form restricted to GL2×ℝ+.
References
SHOWING 1-10 OF 31 REFERENCES
The Central value of the Rankin–Selberg L-Functions
- Mathematics
- 2008
Abstract.Let f be a Maass form for SL$$(3, {\mathbb{Z}})$$ which is fixed and uj be an orthonormal basis of even Maass forms for SL$$(2, {\mathbb{Z}})$$, we prove an asymptotic formula for the…
Automorphic Forms and L-Functions for the Group Gl(n, R)
- Mathematics
- 2006
Introduction 1. Discrete group actions 2. Invariant differential operators 3. Automorphic forms and L-functions for SL(2,Z) 4. Existence of Maass forms 5. Maass forms and Whittaker functions for…
Low lying zeros of families of L-functions
- Mathematics
- 1999
In Iwaniec-Sarnak [IS] the percentages of nonvanishing of central values of families of GL_2 automorphic L-functions was investigated. In this paper we examine the distribution of zeros which are at…
The spectral mean value for linear forms in twisted coefficients of cusp forms
- Mathematics
- 1995
according to whether uj(z) is even or odd, where Kν is the K-Bessel function. The Weyl law (proved by A. Selberg [14], see also [4]) (3) ]{j : tj ≤ T} ∼ T 2/12 shows that there are infinitely many…
Automorphic distributions, L-functions, and Voronoi summation for GL(3)
- Mathematics
- 2004
This paper is third in a series of three, following "Summation Formulas, from Poisson and Voronoi to the Present" (math.NT/0304187) and "Distributions and Analytic Continuation of Dirichlet Series"…
Estimates for Rankin–Selberg L-Functions and Quantum Unique Ergodicity
- Mathematics
- 2001
Abstract Subconvex bounds in the weight aspect for Rankin–Selberg L -functions associated to two cusp forms are established. These bounds are applied to prove the equidistribution of mass conjecture…
Rankin-Selberg without unfolding and bounds for spherical Fourier coefficients of Maass forms
- Mathematics
- 2005
In this paper we study periods of automorphic functions. We present a new method which allows one to obtain non-trivial spectral identities for weighted sums of certain periods of automorphic…
The square mean of Dirichlet series associated with cusp forms
- Mathematics
- 1982
Let be a cusp form of even integral weight k > 2 for the full modular group. Then the Dirichlet series is absolutely convergent for σ > ½( k + 1). Hecke showed that L F is an entire function of s…
The orthogonality of Hecke eigenvalues
- MathematicsCompositio Mathematica
- 2007
In this paper, we study the orthogonalities of Hecke eigenvalues of holomorphic cusp forms. An asymptotic large sieve with an unusually large main term for cusp forms is obtained. A family of special…
Uniform Bound for Hecke L-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…