Bounds on Faltings's delta function through covers

DOI10.4007/annals.2009.170.1zbMath1169.14020OpenAlexW2138978086MaRDI QIDQ2389209

Jürg Kramer, Jay A. Jorgenson

Publication date: 15 July 2009

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: http://annals.math.princeton.edu/annals/2009/170-1/p01.xhtml

zbMATH Keywords

Faltings heighthyperbolic heat kernelsFaltings deltaSelberg zeta

Mathematics Subject Classification ID

Structure of modular groups and generalizations; arithmetic groups (11F06) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Arithmetic varieties and schemes; Arakelov theory; heights (14G40) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (18)

Uniform Sup-Norm Bounds on Average for Cusp Forms of Higher Weights ⋮ An effective bound for the Huber constant for cofinite Fuchsian groups ⋮ Bounding sup-norms of cusp forms of large level ⋮ New explicit formulas for Faltings' delta-invariant ⋮ Remarks on a conjecture of Lang ⋮ Vortex on surfaces and Brownian motion in higher dimensions: special metrics ⋮ An effective Arakelov-theoretic version of the hyperbolic isogeny theorem ⋮ Arakelov self-intersection numbers of minimal regular models of modular curves \(X_0(p^2)\) ⋮ Effective bounds for Faltings's delta function ⋮ Self-intersection of the relative dualizing sheaf on modular curves \(X_{ 1 }(N)\) ⋮ Asymptotic behavior of the Selberg zeta functions for degenerating families of hyperbolic manifolds ⋮ Bounds for canonical Green's function at cusps ⋮ Non-completeness of the Arakelov-induced metric on moduli space of curves ⋮ Semi-stable models of modular curves \(X_0(p^2)\) and some arithmetic applications ⋮ The effective Shafarevich conjecture for abelian varieties of -type ⋮ Effective bounds for Huber’s constant and Faltings’s delta function ⋮ A relation of two metrics on a noncompact hyperbolic Riemann orbisurface ⋮ Bounds for Green's functions on noncompact hyperbolic Riemann orbisurfaces of finite volume

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