scientific article

zbMath0934.14016MaRDI QIDQ3125872

Ahmed Abbes, Emmanuel Ullmo

Publication date: 18 November 1998

Full work available at URL: https://www.digizeitschriften.de/dms/resolveppn/?PPN=GDZPPN00221444X

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

zbMATH Keywords

Green functionsEisenstein seriesSelberg zeta-functionArakelov theorymodular curvearithmetic surfacedualizing sheafasymptotic upper boundsasymptotic lower bound for \(\omega^2\)

Mathematics Subject Classification ID

Arithmetic aspects of modular and Shimura varieties (11G18) [https://zbmath.org/classification/?q=cc:11G30 Curves of arbitrary genus or genus ( e 1) over global fields (11G30)] Modular and Shimura varieties (14G35) Arithmetic varieties and schemes; Arakelov theory; heights (14G40)

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Bounds on Faltings's delta function through covers ⋮ Comparison of Arakelov and Poincaré metrics on \(X_0(N)\) ⋮ The minimal regular model of a Fermat curve of odd squarefree exponent and its dualizing sheaf ⋮ An effective Arakelov-theoretic version of the hyperbolic isogeny theorem ⋮ Arakelov self-intersection numbers of minimal regular models of modular curves \(X_0(p^2)\) ⋮ Self-intersection of the relative dualizing sheaf on modular curves \(X_{ 1 }(N)\) ⋮ A nonsplit sum of coefficients of modular forms ⋮ Bounds for canonical Green's function at cusps ⋮ Semi-stable models of modular curves \(X_0(p^2)\) and some arithmetic applications ⋮ Arakelov computations in genus 3 curves ⋮ Lower bounds on the arithmetic self-intersection number of the relative dualizing sheaf on arithmetic surfaces

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