A mean value theorem for the square of class number times regulator of quadratic extensions

DOI10.5802/aif.2363zbMath1231.11111arXivmath/0410531OpenAlexW1597667499MaRDI QIDQ931897

Takashi Taniguchi

Publication date: 4 July 2008

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0410531

zbMATH Keywords

quaternion algebradensity theoremprehomogeneous vector spacelocal zeta function

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Prehomogeneous vector spaces (11S90) Zeta functions and (L)-functions (11S40)

Related Items (2)

On the zeta functions of prehomogeneous vector spaces for a pair of simple algebras ⋮ How many rational points does a random curve have?

Uses Software

• Maple

Cites Work

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• Arithmétique des algèbres de quaternions
• Prehomogeneous vector spaces and field extensions
• The mean value of the product of class numbers of paired quadratic fields. II.
• The distribution of values of \(L(1,\chi_d)\)
• Basic number theory.
• The mean value of the product of class numbers of paired quadratic fields. III.
• The mean value of the product of class numbers of paired quadratic fields. I
• On the zeta functions of prehomogeneous vector spaces for a pair of simple algebras
• Uniform distribution of the Steinitz invariants of quadratic and cubic extensions
• On proportional constants of the mean value of class numbers of quadratic extensions
• The adelic zeta function associated to the space of binary cubic forms. II: Local theory.
• Density of discriminants of cubic extensions.
• Momente der Klassenzahlen binärer quadratischer Formen mit ganzalgebraischen Koeffizienten

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