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
View PDF on arXiv
13 Citations
Highly Influential Citations
1
Background Citations
4
Methods Citations
1
Results Citations
1

13 Citations

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Citation Type

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 $L(\half,g\times f)L(\half,f)$.…
The second moment of GL(4)×GL(2) L-functions at special points
Non-vanishing of derivatives of (3)×(2) -functions
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
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
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
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.
Automorphic spectral identities and applications to automorphic L-functions on GL2
Rankin–Selberg periods for spherical principal series
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
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
Abstract We prove a sharp upper bound on the L2 norm of a GL3 Maass form restricted to GL2×ℝ+.
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References

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The square mean of Dirichlet series associated with cusp forms
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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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