Displaying similar documents to “On traces of the Brandt-Eichler matrices”

A generalization of Eichler's trace formula.

Juliusz Brzezinski (1997)

Collectanea Mathematica

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Eichler's trace formula for traces of the Brandt-Eichler matrices is proved for arbitrary totally definite orders in central simple algebras of prime index over global fields. A formula for type numbers of such orders is proved as an application.

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 ∈ 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 [ - c f N ] , where c f ∈ R is a constant depending only on f . We give an algebraic proof of a classical result of H. Maass...

Cryptography based on number fields with large regulator

Johannes Buchmann, Markus Maurer, Bodo Möller (2000)

Journal de théorie des nombres de Bordeaux

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We explain a variant of the Fiat-Shamir identification and signature protocol that is based on the intractability of computing generators of principal ideals in algebraic number fields. We also show how to use the Cohen-Lenstra-Martinet heuristics for class groups to construct number fields in which computing generators of principal ideals is intractable.