Uniform Sup-Norm Bounds on Average for Cusp Forms of Higher Weights

DOI10.1007/978-3-319-43648-7_6zbMath1402.11061arXiv1305.1348OpenAlexW1480911804MaRDI QIDQ5278321

Jürg Kramer, Joshua S. Friedman, Jay A. Jorgenson

Publication date: 19 July 2017

Published in: Arbeitstagung Bonn 2013 (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.1348

zbMATH Keywords

cusp formsPetersson inner productFuchsian subgroup

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Holomorphic modular forms of integral weight (11F11) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35)

Related Items (19)

Bounds for eigenforms on arithmetic hyperbolic 3-manifolds ⋮ Construction of Poincaré-type Series by Generating Kernels ⋮ On the Kähler metrics over \(\operatorname{Sym}^d(X)\) ⋮ Bounds on sup-norms of half-integral weight modular forms ⋮ Relating Siegel cusp forms to Siegel-Maaß forms ⋮ Off-diagonal estimates of the Bergman kernel on hyperbolic Riemann surfaces of finite volume ⋮ Analytic properties of spherical cusp forms on \(\mathrm{GL}(n)\) ⋮ Estimates of cusp forms for certain cocompact arithmetic subgroups ⋮ Quotient of Bergman kernels on punctured Riemann surfaces ⋮ Supnorm of modular forms of half-integral weight in the weight aspect ⋮ Estimates of the Bergman kernel on a hyperbolic Riemann surface of finite volume. II ⋮ Bergman kernels on punctured Riemann surfaces ⋮ Estimates of automorphic cusp forms over quaternion algebras ⋮ The heat kernel of a weighted Maass-Laplacian with real weights ⋮ Heat kernel approach for sup-norm bounds for cusp forms of integral and half-integral weight ⋮ Global automorphic Sobolev theory and the automorphic heat kernel ⋮ Uniform bounds on sup-norms of holomorphic forms of real weight ⋮ On the minimal distance between elliptic fixed points for geometrically finite Fuchsian groups ⋮ Effective sup-norm bounds on average for cusp forms of even weight

Cites Work

• Effective bounds for Faltings's delta function
• Mass equidistribution for Hecke eigenforms
• Remarks on a conjecture of Lang
• An approach to the Selberg trace formula via the Selberg zeta-function
• Points of small height on the modular curves \(X_0(N) \)
• Bounding the sup-norm of automorphic forms
• Equidistribution of Hecke eigenforms on the arithmetic surface \(\Gamma_0(N)\setminus {\mathbb H}\).
• Convergence theorems for relative spectral functions on hyperbolic Riemann surfaces of finite volume
• Comparison of Arakelov and Poincaré metrics on \(X_0(N)\)
• On the sup-norm of Maass cusp forms of large level. III
• An effective proof of the hyperelliptic Shafarevich conjecture
• Bounds on Faltings's delta function through covers
• Polynomial bounds for Arakelov invariants of Belyi curves. With an appendix by Peter Bruin.
• Large values of modular forms
• An arithmetic Hilbert–Samuel theorem for singular hermitian line bundles and cusp forms
• Integral points on moduli schemes of elliptic curves
• Fourier coefficients of the resolvent for a Fuchsian group.
• Mass equidistribution for Hecke eigenforms
• Completeness relations for Maass Laplacians and heat kernels on the super Poincaré upper half-plane
• Unnamed Item

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