Bounds for Rankin–Selberg integrals and quantum unique ergodicity for powerful levels

DOI10.1090/S0894-0347-2013-00779-1zbMath1322.11051arXiv1205.5534OpenAlexW2049006851MaRDI QIDQ2862636

Abhishek Saha, Ameya Pitale, Paul D. Nelson

Publication date: 18 November 2013

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.5534

Mathematics Subject Classification ID

Holomorphic modular forms of integral weight (11F11) Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity (58J51)

Related Items (27)

Bounds for eigenforms on arithmetic hyperbolic 3-manifolds ⋮ Zeros of Rankin-Selberg \(L\)-functions at the edge of the critical strip ⋮ Hybrid sup-norm bounds for Maass newforms of powerful level ⋮ Fourier-Jacobi periods and the central value of Rankin-Selberg \(L\)-functions ⋮ Equidistribution in shrinking sets and \(L^4\)-norm bounds for automorphic forms ⋮ Voronoï summation via switching cusps ⋮ Explicit refinements of Böcherer's conjecture for Siegel modular forms of squarefree level ⋮ On sup-norms of cusp forms of powerful level ⋮ The fourth moment of Dirichlet \(L\)-functions along a coset and the Weyl bound ⋮ Explicit Burgess-like subconvex bounds for \(\mathrm{GL_2 \times GL_1}\) ⋮ On weak Mellin transforms, second degree characters and the Riemann hypothesis ⋮ Restrictions of Eisenstein series and Rankin-Selberg convolution ⋮ AUTOMORPHIC SL ₂ ‐PERIODS AND THE SUBCONVEXITY PROBLEM FOR GL ₂ × GL ₃ ⋮ Anticyclotomic \(p\)-adic \(L\)-functions and Ichino's formula ⋮ On the ramification of modular parametrizations at the cusps ⋮ Zeros of newform Eisenstein series on \(\Gamma_{0}(N)\) ⋮ Microlocal lifts and quantum unique ergodicity on \(\mathrm{GL}_2(\mathbb Q_p)\) ⋮ Special value formula for the twisted triple product \(L\)-function and an application to the restricted \(L^2\)-norm problem ⋮ Quantum unique ergodicity for Eisenstein series in the level aspect ⋮ Some analytic aspects of automorphic forms on \(\mathrm{GL}(2)\) of minimal type ⋮ Quantum unique ergodicity for half-integral weight automorphic forms ⋮ Relative trace formulas and subconvexity estimates for $L$-functions of Hilbert modular forms ⋮ On Kuznetsov-Bykovskii's formula of counting prime geodesics ⋮ Subconvex equidistribution of cusp forms: reduction to Eisenstein observables ⋮ An explicit conductor formula for \(\operatorname{GL}_n\times\operatorname{GL}_1\) ⋮ Exact double averages of twisted \(L\)-values ⋮ Mass equidistribution on the torus in the depth aspect

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