On the resolution of cusp singularities and the Shintani decomposition in totally real cubic number fields

DOI10.1007/BF01359864zbMath0403.14005WikidataQ110857006 ScholiaQ110857006MaRDI QIDQ1256014

A. T. Vasquez, Emery Thomas

Publication date: 1979

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/163345

zbMATH Keywords

Hilbert modular varietytotally real cubic number fieldsevaluation of zeta-functionfamily of cubicsresolution of cusp singularitiesShintani decomposition

Mathematics Subject Classification ID

Singularities of surfaces or higher-dimensional varieties (14J17) (3)-folds (14J30) Cubic and quartic extensions (11R16) Global ground fields in algebraic geometry (14G25) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41) Special surfaces (14J25) Totally real fields (11R80)

Related Items

Effective resolution of cusps on Hilbert modular varieties ⋮ Trace and norm of indecomposable integers in cubic orders ⋮ Colmez cones for fundamental units of totally real cubic fields ⋮ Attractor-repeller construction of Shintani domains for totally complex quartic fields ⋮ Computing Shintani domains ⋮ Diophantine equations arising from cubic number fields ⋮ Explicit resolutions of cubic cusp singularities ⋮ Constructing multidimensional periodic continued fractions in the sense of Klein ⋮ The canonical contact structure on the link of a cusp singularity ⋮ The arithmetic genus of Hilbert modular varieties over non-Galois cubic fields ⋮ Higher dimensional analogues of periodic continued fractions and cusp singularities ⋮ Nonvanishing of twists of -functions attached to Hilbert modular forms ⋮ Shintani cones for complex cubic number fields

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On resolutions of cyclic quotient singularities
• Formal ring of a cubic solid angle
• Hilbert modular surfaces
• On the arithmetic of tube domains (blowing-up of the point at infinity)
• Algebraic Number-Fields with two Independent Units
• Einheiten für eine allgemeine Klasse total reeller algebraischer Zahlkörper.