Subconvexity for sup-norms of cusp forms on \(\mathrm{PGL}(n)\)

DOI10.1007/s00029-015-0219-5zbMath1352.11054OpenAlexW2253117354MaRDI QIDQ739817

Valentin Blomer, Péter Maga

Publication date: 22 August 2016

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00029-015-0219-5

zbMATH Keywords

Diophantine approximationtrace formulaHecke operatorsamplification\(\mathrm{GL}(n)\)sup-norms

Mathematics Subject Classification ID

Other groups and their modular and automorphic forms (several variables) (11F55) Diophantine inequalities (11D75) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items (13)

Analytic properties of spherical cusp forms on \(\mathrm{GL}(n)\) ⋮ Spectral aspect subconvex bounds for \(U_{n+1} \times U_n\) ⋮ Supnorm of an eigenfunction of finitely many Hecke operators ⋮ Optimal Diophantine exponents for \(\mathrm{SL}(n)\) ⋮ Hybrid bounds for the sup-norm of automorphic forms in higher rank ⋮ The sup-norm problem for automorphic cusp forms of 𝑃𝐺𝐿(𝑛,ℤ[𝕚)] ⋮ Group actions and harmonic analysis in number theory. Abstracts from the workshop held May 7--12, 2023 ⋮ On the global sup-norm of \(\mathrm{GL}(3)\) cusp forms ⋮ The amplification method in the context of \(\mathrm{GL}(n)\) automorphic forms ⋮ Large values of cusp forms on \(\mathrm{GL}_n\) ⋮ Subconvex bounds for Hecke-Maass forms on compact arithmetic quotients of semisimple Lie groups ⋮ Explicit subconvexity savings for sup-norms of cusp forms on \(\mathrm{PGL}_n(\mathbb{R})\) ⋮ Beyond the spherical sup-norm problem

Cites Work

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• Large values of cusp forms on \(\mathrm{GL}_n\)
• The sup-norm problem on the Siegel modular space of rank two
• The amplification method in the GL(3) Hecke algebra
• Recent progress on the quantum unique ergodicity conjecture
• Recent developments in mathematical Quantum Chaos
• The Sup-Norm Problem for PGL(4)
• On the Linear Independence of Fractional Powers of Integers

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