## 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…

COMPOSITIO MATHEMATICA The L 2 restriction norm of a GL 3 Maass form

- Mathematics
- 2012

We prove a sharp upper bound on the L 2 norm of a GL 3 Maass form restricted to GL 2 × R + .

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…

## References

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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…

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 cubic moment of central values of automorphic L-functions

- Mathematics
- 1998

The authors study the central values of L-functions in certain families; in particular they bound the sum of the cubes of these values.Contents:

Estimates for coefficients of L -functions. III

- Mathematics
- 1994

In this sequence of papers we investigate Dirichlet series
$${\rm A}(s,X) = \sum\limits_1^\infty {{a_n}} X(n){n^{ - 3}}$$
(1)
having Euler products and compatible functional equations with…

Some Extremal Functions in Fourier Analysis, III

- Mathematics
- 1985

We obtain the best approximation in L1(ℝ), by entire functions of exponential type, for a class of even functions that includes e−λ|x|, where λ>0, log |x| and |x|α, where −1<α<1. We also give…