Forms representable by integral binary quadratic forms
Philip Leonard, Kenneth Williams (1974)
Acta Arithmetica
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Philip Leonard, Kenneth Williams (1974)
Acta Arithmetica
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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.
Elise Björkholdt (2000)
Journal de théorie des nombres de Bordeaux
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Let be a totally real algebraic number field whose ring of integers is a principal ideal domain. Let be a totally definite ternary quadratic form with coefficients in . We shall study representations of totally positive elements by . We prove a quantitative formula relating the number of representations of by different classes in the genus of to the class number of , where is a constant depending only on . We give an algebraic proof of a classical result of H. Maass...
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.
Bill Dulin, Hubert Butts (1972)
Acta Arithmetica
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Paul Ponomarev (1976)
Acta Arithmetica
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A. Arenas, P. Bayer (2000)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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Stéphane Louboutin, Hee-Sun Yang, Soun-Hi Kwon (2004)
Mathematica Slovaca
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