The L2 restriction norm of a GL3 Maass form

DOI10.1112/S0010437X11007366zbMath1287.11066arXiv1212.4002MaRDI QIDQ2894200

Xiaoqing Li, Matthew P. Young

Publication date: 29 June 2012

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.0195

zbMATH Keywords

automorphic formrestriction norm\(\mathrm{GL}_3\) Maass form

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Other groups and their modular and automorphic forms (several variables) (11F55) Other Dirichlet series and zeta functions (11M41) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items (8)

A symplectic restriction problem ⋮ Parametrization of Kloosterman sets and \(\mathrm{SL}_3\)-Kloosterman sums ⋮ The \(L^2\) restriction norm of a Maass form on \(\mathrm{SL}_{n+1}(\mathbb {Z})\) ⋮ Special value formula for the twisted triple product \(L\)-function and an application to the restricted \(L^2\)-norm problem ⋮ The second moment of \(\mathrm{GL} (3) \times \mathrm{GL} (2)\) \(L\)-functions at special points from \(\mathrm{GL} (3)\) forms ⋮ The Relative Trace Formula in Analytic Number Theory ⋮ The second moment of \(\mathrm{GL} (4) \times \mathrm{GL} (2)\) \(L\)-functions at special points ⋮ Subconvexity and equidistribution of Heegner points in the level aspect

Cites Work

• Unnamed Item
• Large values of eigenfunctions on arithmetic hyperbolic surfaces
• The second moment of \(\text{GL}(3)\times\text{GL}(2)\) \(L\)-functions, integrated
• On explicit integral formulas for \(\text{GL}(n, \mathbb R)\)-Whittaker functions. With an appendix by Daniel Bump, Solomon Friedberg, and Jeffrey Hoffstein
• Bounding sup-norms of cusp forms of large level
• Rank lowering linear maps and multiple Dirichlet series associated to \(\text{GL}(n,\mathbb R)\)
• Automorphic distributions, \(L\)-functions, and Voronoi summation for \(\text{GL}(3)\)
• On \(L^{\infty }\) norms of holomorphic cusp forms
• Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds
• Restriction of toral eigenfunctions to hypersurfaces
• Automorphic forms on \(GL(3)\). I, II
• The behaviour of eigenstates of arithmetic hyperbolic manifolds
• Coefficients of Maass forms and the Siegel zero. Appendix: An effective zero-free region, by Dorian Goldfeld, Jeffrey Hoffstein and Daniel Lieman
• The subconvexity problem for \(\mathrm{GL}_2\)
• \(L^ \infty\) norms of eigenfunctions of arithmetic surfaces
• Zeros of principal \(L\)-functions and random matrix theory
• Second order average estimates on local data of cusp forms
• A large sieve density estimate near \(\sigma = 1\)
• On the existence and temperedness of cusp forms for SL3(Z)
• Rankin-Selberg Convolutions
• Lp norm estimates of eigenfunctions restricted to submanifolds
• Barnes' Second Lemma and its Application to Rankin-Selberg Convolutions
• On the Decomposition of a Representation of SO_n When Restricted to SO_n-1
• A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$
• Spectra of hyperbolic surfaces
• Hypergeometric Series and Euler Factors at Infinity for L-Functions on GL(3, R )×GL(3, R )
• Can One Hear the Shape of a Drum?
• On the sup-norm of Maass cusp forms of large level

This page was built for publication: The L² restriction norm of a GL₃ Maass form