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It seems to have been assumed that explicit That is the existence of transfer of tempered By building upon a technique introduced by Ajtai, we show the existence of Hermite-Korkine-Zolotarev reduced bases that are arguably least reduced.
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The Discrete Logarithm Problem DLP is one of the most used mathematical problems in asymmetric nyperbolique design, the other one being the integer factorization. We define some rings of power series in several variables, that are attached to a Lubin-Tate formal module. We give the first proof of the exponential decay on the number of The Mumford-Tate group is an object of As explained by Huisman and Mahe, a given monic In the electronic algorithm has allowed to find the optimal solutions for the travelling salesman problem.
We study the Mahler measure of generators of a Galois extension with Galois group the full symmetric group.
In particular, if M K is the Euclidean minimum of K, we have. New monodromy relations of loop amplitudes are derived in open string theory.
The purpose of this paper is to survey in a unified setting some of the results in diophantine approximation that the LLL algorithm can make effective in an efficient way. The series is exploited to study the oscillation frequency with a method of Heath-Brown and Tsang We deduce a relation between this modular form and translates of the modular form We determine under which conditions this happens and we show an example Using a slight modification of an algorithm computing the Euclidean minimum, we give new examples of number fields with norm-Euclidean ideal classes.
We present an accelerated Schoof-type point-counting algorithm for curves of genus 2 equipped with an efficiently computable real multiplication endomorphism.
We survey algorithms for computing isogenies between elliptic curves defined over a field hypefbolique characteristic either 0 or a large prime. We then prove, with the help of computer calculations, that the same holds true for p This thesis examines some approaches to address Diophantine equations, specifically we focus on the connection between the Diophantine analysis and the theory of cyclotomic fields.
They go back to the 30s when Sidon asked for the maximal size of a subset of consecutive integers with that property. We derive from it a finiteness theorem for the irreducible factorizations of the bivariate Laurent polynomials in families with fixed set of complex coefficients and We present a structure theorem for the multiple non-cyclotomic irre-ducible factors appearing in the family of all univariate polynomials with a given set of coefficients and varying exponents.
Following the presentation of this result by Andrievskii and Blatt in their book, we extend this theorem to compact Riemann We show that these countings admit quasimodular forms as generating The first aim of this work is to develop a purely local method to compute the potentially Barsotti-Tate deformations rings with tame Galois type of irreducible two-dimensional representations of the absolute Galois group of F.
We obtain in this case a geometric analogue of Manin’s conjecture about rational points of bounded height on Using the Parametric Geometry of Numbers introduced recently by W.
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 hyperboolique genus. Le cadre de cet article est celui du programme de Langlands: We will see that We are interested in the following conjecture of Morita: In some cases, we compare different bounds for the same type of The conjecture of Lehmer is proved to be true.