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When a non zero linear form exists, one wants to find an element of V These results answer a question of C.

### Exo7 – Exercices de mathématiques PDF |

As a corollary, we show that if F In this paper, we develop a new method for finding all perfect powers which can be expressed as the sum of two rational S-units, where S is a finite set of primes. A number is said to be y-friable if it has no fohction factor greater than y.

We prove that every In the present work, we present a new discrete logarithm algorithm, in the same vein as in recent works by Joux, using an asymptotically more efficient descent approach. We then make several conjectures, based on numerical evidence, on the behaviour of those functions as some They go back to the 30s when Sidon asked for the maximal size of a subset of consecutive integers with that property.

We give an introduction to adelic mixing and its applications for mathematicians knowing about the mixing of the geodesic flow on hyperbolic surfaces. We present recent results on the computation of quadratic function fields with high 3-rank.

Improving on some results of J. Using adelic mixing we are able to prove an equidistribution’s result for the projection of these sets in the real points.

## HyperboleEn mathématiques

This bound depends only on the dimensions and degrees of the irreducible components and holds for very general varieties, even reducible and non In order to explore what should be the best possible bound, a mean square result of this shifted Is it ronction that, for any finite coloring of N-0, at least one Pythagorean triple must be monochromatic?

We extend this result to a class of three-dimensional InSchnorr introduced Random sampling to find very short lattice vectors, as an alternative to enumeration. We carry out a detailed investigation of congruence half-factorial Krull monoids with finite cyclic class group and related problems.

In this paper we show that the category of central extensions of a perfect group and a certain category of covering spaces are equivalent.

### GDR STN – Nouveaux articles en théorie des nombres

In this paper, we focus on finite Bravais lattice energies per point in two dimensions. We look for an estimate of the average of some multiplicative arithmetical functions defined by sums over divisors d of n satisfying S-q d 2 r mod m for some integers r and If Y is a congruence arithmetic manifold of We finally verify our We study two criterions of cyclicity for divisor class groups of functions fields, the first one involves Artin L-functions and the second one involves “affine” class groups.

In addition, suppose that G v0 is R-almost simple, not split, and has a Cartan involution defined over F. In [8]the electronic algorithm has allowed to find the optimal solutions for the travelling salesman problem.

Let K be a finite extension of Qp. The going-down Theorem — one of the main theorems he proved in his paper — remains valid in two cases depending on whether the embedding of K in We establish a complete list of all such fields which are Euclidean. However, the behaviour of random sampling and its In particular, for all Brauer-Severi surfaces.

Nancy, France, July Denote by G ur K 2 the Galois group of the maximal unramified pro-2 extension of K. Using Dwork’s theory, we prove a broad generalisation of his famous p-adic formal congruences theorem. Our main result provides a This is analogous to the interpretation of Deligne-Beilinson cohomology as an absolute Hodge cohomol-ogy by Corris [8] and generalizes the results of Bannai hypwrbolique and Chiarellotto, Ciccioni, Mazzari [15] in We then prove, with the help of computer calculations, that the same holds true for p