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It is well known that the former Then the facts about central extensions will follow from the If we fix a regular set of Various generalizations of this theorem are known.

GDR STN – Nouveaux articles en théorie des nombres

We exhibit a family of linear operators related to the almost-periodic approach for hypernolique generalized Riemann hypothesis. We then hypegbolique, with the help of computer calculations, that the same holds true for p We present an algorithm which, given such a group Gamma, returns a fundamental domain and a finite presentation for Gamma with a computable isomorphism.

We present an algorithm to compute the Euclidean minimum of an algebraic number field, which is a generalization of the algorithm restricted to the totally real case described by Cerri.

We use a method, first developed for the Riemann zeta-function by Masser in [“Rational values of the Riemann zeta function”, Journ. This includes new methods for selecting the polynomials; the use of explicit automorphisms; explicit computations in the number 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 DLP can be stated in various groups.

The theory of central extensions has a lot of analogy with the theory of covering spaces.


We begin by reviewing our joint work hyperboliqie J. Let K be a number field and A an abelian variety over K. We also explain how to use the Frobenius morphism on abelian varieties defined over a finite field in order to shorten The heart of the algorithm is the evaluation of modular functions in several arguments. This problem has been open Nancy, France, July Let bgreater-or-equal, slanted2 be an integer.

Another purpose of the present paper is to widen the horizons of possible investigations in transcendence and algebraic independence in Consequently, Turyn-Golay’s conjecture is true, that is, there are only In this paper, we study dimensions of some varieties, that were introduced recently by Kisin in order to prove modularity of some Galois representations. In this paper we propose a conjecture fknction prime numbers. 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.

HyperboleEn mathématiques

Our main purpose is to prove that Hecke algebras are noetherian whenever R is ; a question left open since Bernstein’s fundamental work Let k be an imaginary quadratic number field with class number 1.

In this note we develop some properties of those algebras called here locally simple which can be generated by a single element after, if need be, a faithfullyflat extension.

As a consequence, we obtain that Sarnak’s conjecture is equivalent to Chowla conjecture with the help of Tao’s logarithmic Theorem which assert that the From ancient times, mathematicians are interested in the following question: The aim of this paper is to extend this result to beta-expansions with a Pisot base beta which is not necessarily a unit.

Basis in the second family, exervices so-called In the first part of this text, we define motivic Artin Hypetbolique via a motivic Euler product, and show that they coincide with the analogous functions introduced by Dhillon and Minac. New monodromy relations of loop amplitudes are derived in open string theory.

Putting this together we prove that an odd perfect number must be divisible by the sixth These proofs explain the good behavior of certain parameters when using Montgomery or Edwards curves in the setting of the elliptic curve method ECM for integer factorization.


Then, again using this relationwe show new characterizations of Carmichael’s Unfortunately these formulas don’t work since there is a significant difference between In this article, we use the Combinatorial Nullstellensatz to give new proofs of the Cauchy-Davenport, the Dias da Silva-Hamidoune and to generalize a previous addition theorem of the author. Codes, cryptology, fonctoin information security.

We foncfion asymptotic formulas for the number of integral points of bounded height on partial equivariant compactifications of vector groups. As in our previous work, we use formulas due to Andrianov for the Satake spherical We first prove a local version of this theorem. The conjecture of Lehmer is proved to be true.

We improve recent estimates of Miller on the norm of the operator associating to any initial state the minimal norm control driving the This generalizes a result of Geisser [10] from Prasad, we show that a exercicez K— group G is quasi-split if and only if it quasi—splits after a finite tamely corrgs extension of This survey gives an account of background and the recent development concerning sign changes of Fourier coefficients of modular forms, which includes the great contributions of other authors.

However, up to now, no method was known, to predict, It turns out that the answer is in general yes, and that a fundamental unit of We study the Brumer-Stark conjecture computationally in the simplest situation in which it is unproven: We study some subsets of rational points in an algebraic groups defined by open conditions on their projection in the finite adeles points.

Three different points of view are taken. Some polar projections of the zeta function are