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  • [hal-01081277] On the representation of friable integers by linear forms

    14 août, par Armand Lachand
    Let $P^+(n)$ denote the largest prime of the integer $n$. Using the \beginalign* \Psi_F_1\cdots F_t\left(\mathcalK\cap[-N,N]^d,N^1/u\right):= \#\left\\mathcalK\in \mathbfN\cap[-N,N]^d:\vphantomP^+(F_1(\boldsymboln)\cdots F_t(\boldsymboln))\leq N^1/u\right. \left.P^+(F_1(\boldsymboln)\cdots (...)
  • [hal-01283042] Series Representation of Power Function

    10 août, par Kolosov Petro
    In this paper described numerical expansion of natural-valued power function $x^n$, in point $x=x_0$ where $n, \ x_0$ - natural numbers. Applying numerical methods, that is calculus of finite differences, namely, discrete case of Binomial expansion is reached. Received results were compared (...)
  • [hal-01283042] Series Representation of Power Function

    9 août, par Kolosov Petro
    In this paper described numerical expansion of natural-valued power function $x^n$, in point $x=x_0$ where $n, \ x_0$ - natural numbers. Applying numerical methods, that is calculus of finite differences, namely, discrete case of Binomial expansion is reached. Received results were compared (...)
  • [hal-01568373] Breaking DLP in $GF(p^5)$ using 3-dimensional sieving

    3 août, par Laurent Grémy, Aurore Guillevic, François Morain
    We report on a discrete logarithm computation in $GF(p^5)$ for a 20-decimal digit prime, using the number field sieve algorithm (NFS-DL), and a relation collection phase over degree-two polynomials, instead of the more classical degree-one (...)
  • [hal-01569570] Sur la comparaison entre les minima et les pentes

    1er août, par Huayi Chen
    On étudie la comparaison entre les minima et les pentes successifs d'un fibré vectoriel hermitien sur une courbe arithmétique et démontre un encadrement uniform de leurs différences.

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