On \(L^{\infty }\) norms of holomorphic cusp forms

DOI10.1016/j.jnt.2006.09.003zbMath1121.11038OpenAlexW2042812391MaRDI QIDQ880057

Honggang Xia

Publication date: 10 May 2007

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2006.09.003

zbMATH Keywords

cusp formHecke eigenformDeligne's theorem

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Holomorphic modular forms of integral weight (11F11) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items (16)

The L² restriction norm of a GL₃ Maass form ⋮ An omega result for supremum norms of Hecke-eigenforms in the level aspect ⋮ Bounding sup-norms of cusp forms of large level ⋮ An arithmetic Hilbert–Samuel theorem for singular hermitian line bundles and cusp forms ⋮ Analytic properties of spherical cusp forms on \(\mathrm{GL}(n)\) ⋮ On sup-norms of cusp forms of powerful level ⋮ Estimates of cusp forms for certain cocompact arithmetic subgroups ⋮ On the size of Ikeda lifts ⋮ Real zeros of holomorphic Hecke cusp forms ⋮ Wide moments of L-functions. I: Twists by class group characters of imaginary quadratic fields ⋮ Jacobi forms, Saito-Kurokawa lifts, their pullbacks and sup-norms on average ⋮ Supnorm of modular forms of half-integral weight in the weight aspect ⋮ Additive twists of Fourier coefficients of modular forms ⋮ Distribution of Maass of holomorphic cusp forms ⋮ Subconvex bounds for Hecke-Maass forms on compact arithmetic quotients of semisimple Lie groups ⋮ Uniform bounds on sup-norms of holomorphic forms of real weight

Cites Work

• \(L^ \infty\) norms of eigenfunctions of arithmetic surfaces
• Unnamed Item

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