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Parametric Solutions of the Diophantine Equation A² + nB⁴ = C³

Susil Kumar Jena (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

The Diophantine equation A² + nB⁴ = C³ has infinitely many integral solutions A, B, C for any fixed integer n. The case n = 0 is trivial. By using a new polynomial identity we generate these solutions, and then give conditions when the solutions are pairwise co-prime.

Paramétrisation de structures algébriques et densité de discriminants

Karim Belabas (2003/2004)

Séminaire Bourbaki

La composition de Gauss donne une structure de groupe aux orbites de formes quadratiques binaires entières de discriminant D , sous l’action de SL 2 par changement de variable, essentiellement le groupe des classes de l’ordre quadratique de discriminant  D . Les domaines fondamentaux associés permettent calculs explicites et évaluation d’ordres moyens. Je présenterai les lois de composition supérieures découvertes par M. Bhargava à partir de la classification des espaces vectoriels préhomogènes réguliers,...

Parametrization of integral values of polynomials

Giulio Peruginelli (2010)

Actes des rencontres du CIRM

We will recall a recent result about the classification of those polynomial in one variable with rational coefficients whose image over the integer is equal to the image of an integer coefficients polynomial in possibly many variables. These set is polynomially generated over the integers by a family of polynomials whose denominator is 2 and they have a symmetry with respect to a particular axis.We will also give a description of the linear factors of the bivariate separated polynomial f ( X ) - f ( Y ) over a...

Parity in Bloch’s conductor formula in even dimension

Takeshi Saito (2004)

Journal de Théorie des Nombres de Bordeaux

For a variety over a local field, Bloch proposed a conjectural formula for the alternating sum of Artin conductor of -adic cohomology. We prove that the formula is valid modulo 2 if the variety has even dimension.

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