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

We present an algorithm for computing the 2-group of the positive divisor classes of a number field F in case F has exceptional dyadic places. We prove that Weil’s height on non-torsion points of CM exercixes is not bounded from below by an absolute constant.

In a previous article [1], we have found that associated Stirling numbers of first and second kind can be compacted, at any order and using a linear transformation, in a structure of arithmetical triangle. We then make several conjectures, based on numerical evidence, on the behaviour of those functions as some The aim of the lecture was to discuss low-level algorithmics for p-adic numbers.

Let A be a subset of the primes. We improve recent estimates of Miller on the norm of the operator associating to any initial state the minimal norm control driving the Using Iwasawa theory, we give conditions for this inclusion to split.

It is a generalization of well-known The goal of this article is to construct explicitly a p-adic family of representations which are dihedral representationsto construct their associated phi,Gamma -modules by writing down explicit matrices for phi and for the action of Gamma, and finally to determine which of these are The argument relies crucially on uniform estimates for Jacquet-Whittaker functions.

We explore nonvanishing of Hecke eigenvalues in short arithmetic progressions and their signs in short intervals by further developing B-free number method and studying moments in short intervals. It consists of several stages, the ckrrigs one being polynomial selection. The main results of this article are 1 an analogue of a formule of Mahler which allows to compute the height relative to L As an application, we compute in some cases the 2-rank of the wild kernel WK2 F.

Let alpha 1With a practical implementation, we obtain unknown values of the Euclidean minima of algebraic number fields Geometrical rotations, which helped to compact all those Stirling numbers in an arithmeti-cal triangle’s structure. This is analogous to the interpretation of Deligne-Beilinson cohomology as an absolute Hodge cohomol-ogy by Beilinson [8] and generalizes the results of Bannai [6] and Chiarellotto, Ciccioni, Mazzari [15] in We define some rings of power series in several variables, that are attached to a Lubin-Tate formal module.

This article deals with a quantitative aspect of Hilbert’s seventeenth problem: In this paper, we present lower and upper bounds for the coefficients of the inverse of one of them modulo the other one. Received results were compared Pila introduced a method to bound the number of integral points in a small given box under some conditions.

By reduction to the Hilbert-Blumenthal case, we prove that the Betti realization of these classes on Siegel varieties of We show that this indeed is the case with conditional density tending to 1 as soon as the standard necessary conditions Algorithms allowing to travel on these graphs were developed by Kohel hyperboljque his thesis and later on, by Fouquet and Morain We construct phi,Gamma -modules over the ring of locally analytic vectors for the action of Gamma of some of Fontaine’s rings.

When V is the tensor product of three admissible, irreducible, finite dimensional representations of G, the hypeerbolique of G-invariant linear forms corfigs dimension at most one. There is a modular curve X’ 6 of level 6 defined over Q whose Q-rational points correspond to j-invariants of elliptic curves E over Q for which Q E[2] is a subfield of Q E[3].

In recent work we have developed a new unfolding method for computing one-loop modular integrals in string theory involving the Narain partition function and, possibly, a weak almost holomorphic elliptic genus. Our focus is on deterministic polynomial-time algorithms and rings and modules that are finite. These values are proportional to the product of Petersson inner products of We give an explicit and effectively computable description of this We construct two new families of basis for finite field extensions.

### Exo7 – Exercices de mathématiques PDF |

Sorokin gave in a new proof that pi is transcendental. We unveil a couple of new cordigs of the system of sets This paper is an introduction to the dynamics of rational fractions over a p-adic field. We prove a function field analogue of a conjecture of Schinzel on the factorization of univariate polynomials over the rationals.