The second moment of GL(3)×GL(2) L-functions, integrated☆

@article{Young2011TheSM,
  title={The second moment of GL(3)×GL(2) L-functions, integrated☆},
  author={Matthew P. Young},
  journal={Advances in Mathematics},
  year={2011},
  volume={226},
  pages={3550-3578}
}
  • M. Young
  • Published 9 March 2009
  • Mathematics
  • Advances in Mathematics
Simultaneous non-vanishing of GL(3) × GL(2) and GL(2) L-functions
  • Rizwanur Khan
  • Mathematics
    Mathematical 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 $L(\half,g\times f)L(\half,f)$.
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References

SHOWING 1-10 OF 31 REFERENCES
The Central value of the Rankin–Selberg L-Functions
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)
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
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
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)
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
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
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
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
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
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
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