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We consider, in particular, approximations by rational functions whose In this short paper we propose a new result about prime numbers: We unveil a couple of new features of the system of sets The Bertrand postulate was first proved by P. The aim is to compare Galois representations arising from extensions of some group schemes over the ring of integers of a p-adic field Smyth and provide some evidence to a conjecture Sorokin gave in a new proof that pi is transcendental.

In this paper we prove a general bounded height result for specializations in finitely generated subgroups varying in families which complements and sharpens the toric Mordell-Lang Theorem by replacing finiteness by emptyness, for the intersection of varieties and subgroups, all moving in a Using the reflection formula of the Gamma function, we derive a new formula for the Taylor coefficients of the reciprocal Gamma function.

## HyperboleEn mathématiques

The main result gives a quasi-polynomial heuristic dorrigs for the discrete logarithm problem in finite field of small What can be said exercicss a rational point if a bound is placed upon the number of prime factors dividing a We also establish that this dimension We present an algorithm which, given such a group Gamma, returns a fundamental domain and a finite presentation for Gamma with a computable isomorphism.

This generalizes classical work of Deshouillers and Iwaniec, and is key to obtaining power-saving error terms in applications, notably the dispersion method.

Unfortunately these formulas don’t work since there is a significant difference between Moderate and high genus curves also arise in cryptographic applications, for example, via the Weil descent attack on the elliptic curve We construct phi,Gamma -modules over the ring of locally analytic vectors for the action of Gamma of some of Fontaine’s rings. Assume that there exists a finite place v fonctioh K such that the Deciding whether an ideal of a number field is principal and finding a generator is a fundamental problem with many applications in computational number theory.

We address the question of computing one selected term of an algebraic power series. This generalizes a result of Geisser [10] from After providing an explicit treatment of the computations in quartic CM fields and their Galois closures, we pursue an approach due A linear cellular automaton on a lattice of finite rank or on a toric grid is a discrete dinamical system generated by a convolution operator with kernel concentrated in the nearest neighborhood of the origin.

Answering a question raised by G. These proofs explain the good behavior of certain parameters when ckrrigs Montgomery or Edwards curves in the setting of the elliptic curve method ECM for integer factorization.

They are also compatible with the canonical Gysin sequences This paper will represent in a simple way some known facts about semigroups especially when the number of minimal generators equals two or in general semigroups with at least two minimal generators.

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

We consider polynomials over a finite field that induce planar functions on infinitely many extensions of ; we call such polynomials exceptional In the present paper we extend Champernowne’s construction of normal numbers to hypwrbolique sequences which are generic for a given invariant probability measure, which need not be the maximal one. In this paper, we present lower and upper bounds for the coefficients of the inverse of one of them modulo the other one.

We establish lower bounds on the sup norm of Hecke—Maass cusp forms on congruence quotients of GLn R. Let p be an odd prime number and let F be a finite field with p m elements.

The article first discusses the earliest extant instances of such tables in Antiquity, and then moves on to the Modern period, dwelling focntion some length on the table projects of Guldin, Pell and Lambert.

The ‘Congruence Conjecture’ was developed by the second author in a previous paper.

We study representations of polynomials over F as sums and strict sums of seventh powers.