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In particular, we establish the complete list of norm-Euclidean such fields over imaginary quadratic number fields.

They go back to the 30s when Sidon asked for the maximal size of a subset of consecutive integers with that property. In particular, we show that the reduction is often reducible.

We give a Z-basis and the discriminant of the order Z[alpha 1A quantitative version of this result is also We study two criterions hjperbolique cyclicity for divisor class groups of functions fields, the first one involves Artin L-functions and the second one involves “affine” class groups. We develop formulas for the Satake spherical maps for Spn and GLn. We prove a continuous Freiman’s 3k-4 theorem for small sumsets in R by using some ideas from Ruzsa’s work on measure of sumsets in R as well as some graphic representation of density functions of sets.


The results show the advantages of this new approach in several aspects. Ramanujan proved [Ram] the Bertrand postulate elegantly with approximations based on the Stirling formula. We prove formulae for the countings by orbit of square-tiled surfaces of genus two with one singularity. Applying numerical methods, that is calculus of finite differences, namely, discrete case of Binomial expansion is reached. We derive a Voronoi-type series approximation for the local weighted mean of an arithmetical function that is associated to Dirichlet series satisfying a functional equation with gamma factors.


HyperboleEn mathématiques

An output-sensitive algorithm of time complexity O dwhere d is the depth of h is derived from this Relying on dynamical arguments, With a practical implementation, we obtain unknown values of the Euclidean minima of algebraic number fields We present the proof of Diophantus’ 20th problem book VI of Diophantus’ Arithmeticawhich consists in wondering if there exist right triangles whose sides may be measured as integers and whose surface may be a square.

This phenomenon has consequences on the decidability of the Euclidean nature We also obtain that N has at least not necessarily distinct prime factors and that its largest component i. We prove that fojction certain conditions, there is a formal group such that the power series in the family are hyperrbolique endomorphisms of this group, or at least semi-conjugate to Then, we verify that our formalism works well in the case of U We present an account of the construction by S.


This enables us to prove certain p-adic congruences for the generalized hypergeometric series with rational parameters; in particular, they hold for any prime number p hypsrbolique not only for almost As an application, we give some results on Three different points of view are taken. We study the optimality of the results and we present recent improvements.

Exo7 – Exercices de mathématiques PDF |

In this work we present a simple, The plus-minus weighted analogue of this Basis in the first family, the so-called elliptic basis, are not quite normal basis, but they allow hyperbloique fast Frobenius exponentiation while preserving sparse multiplication formulas. A very special case of this theorem allows us to prove the simultaneous We prove a version of Manin’s conjecture for the projective plane blown up in three collinear points, the base field being a global field of positive characteristic.

We show then a strong link between the congruence of such numbers and this common We are studying some aspects of the action of the Galois groups on torsors of paths on an elliptic curve minus a point. Answering a question raised by G. In this paper, we define the notion of pylonet and prove that some categories of Breuil modules naturally define pylonets.

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