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  • [hal-01463665] Periodic balanced binary triangles

    7 novembre, par Jonathan Chappelon
    A binary triangle of size $n$ is a triangle of zeroes and ones, with $n$ rows, built with the same local rule as the standard Pascal triangle modulo $2$. A binary triangle is said to be balanced if the absolute difference between the numbers of zeroes and ones that constitute this triangle is (...)
  • [hal-00806923] A generalisation of Miller’s algorithm and applications to pairing computations on abelian varieties

    6 novembre, par David Lubicz, Damien Robert
    In this paper, we use the theory of theta functions to generalize to all abelian varieties the usual Miller's algorithm to compute a function associated to a principal divisor. We also explain how to use the Frobenius morphism on abelian varieties defined over a finite field in order to shorten (...)
  • [hal-01629760] Numerical stability of Euclidean algorithm over ultrametric fields

    6 novembre, par Xavier Caruso
    Nous étudions le problème de la stabilité du calcul des résultants et sous-résultants des polynômes définis sur des anneaux de valuation discrète complets (e.g. ℤ p ou k où k est un corps). Nous démontrons que les algorithmes de type Euclide sont très instables en moyenne et, dans de nombreux cas, nous (...)
  • [hal-00834222] Poisson structures and star products on quasimodular forms

    6 novembre, par François Dumas, Emmanuel Royer
    We construct and classify all Poisson structures on quasimodular forms that extend the one coming from the first Rankin-Cohen bracket on the modular forms. We use them to build formal deformations on the algebra of quasimodular (...)
  • [hal-00905887] Multiplicate inverse forms of terminating hypergeometric series

    6 novembre, par Christian Lavault
    The multiplicate form of Gould--Hsu's inverse series relations enables to investigate the dual relations of the Chu--Vandermonde--Gauß's, the Pfaff--Saalschütz's summation theorems and the binomial convolution formula due to Hagen and Rothe. Several identitity and reciprocal relations are thus (...)

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