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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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