The Hilbert modular group, resolution of the singularities at the cusps and related problems

F. Hirzebruch

Displaying similar documents to “The Hilbert modular group, resolution of the singularities at the cusps and related problems”

On Taylor's conjecture for Kummer orders

Philippe Cassou-Noguès, Anupam Srivastav (1990)

Journal de théorie des nombres de Bordeaux

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A quadratic field of prime discriminant requiring three generators for its class group, and related theory

Daniel Shanks, Peter Weinberger (1972)

Acta Arithmetica

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On integral representations by totally positive ternary quadratic forms

Elise Björkholdt (2000)

Journal de théorie des nombres de Bordeaux

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Let $K$ be a totally real algebraic number field whose ring of integers $R$ is a principal ideal domain. Let $f (x_{1}, x_{2}, x_{3})$ be a totally definite ternary quadratic form with coefficients in $R$ . We shall study representations of totally positive elements $N \in R$ by $f$ . We prove a quantitative formula relating the number of representations of $N$ by different classes in the genus of $f$ to the class number of $R [\sqrt{- c_{f} N}]$ , where $c_{f} \in R$ is a constant depending only on $f$ . We give an algebraic proof of a classical result of H. Maass...