ﻻ يوجد ملخص باللغة العربية
The general number field sieve (GNFS) is the most efficient algorithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. The quality of the chosen polynomials in polynomial selection can be modelled in terms of size and root properties. In this paper, we describe some algorithms for selecting polynomials with very good root properties.
We explore whether a root lattice may be similar to the lattice $mathscr O$ of integers of a number field $K$ endowed with the inner product $(x, y):={rm Trace}_{K/mathbb Q}(xcdottheta(y))$, where $theta$ is an involution of $K$. We classify all pair
Let $F(boldsymbol{x})$ be a diagonal integer-coefficient cubic form in $min{4,5,6}$ variables. Excluding rational lines if $m=4$, we bound the number of integral solutions $boldsymbol{x}in[-X,X]^m$ to $F(boldsymbol{x})=0$ by $O_{F,epsilon}(X^{3m/4 -
We associate to every algebraic number field a hyperbolic surface lamination and an external fundamental group: the latter a generalization of the fundamental germ that necessarily contains external (not first order definable) elements. The external
Most hypersurfaces in projective space are irreducible, and rather precise estimates are known for the probability that a random hypersurface over a finite field is reducible. This paper considers the parametrization of space curves by the appropriat
We obtain an estimate on the average cardinality of the value set of any family of monic polynomials of Fq[T] of degree d for which s consecutive coefficients a_{d-1},..., a_{d-s} are fixed. Our estimate holds without restrictions on the characterist