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This work uses a combinatorial identity involving Stirling’s numbers of the second kind to prove and generalize Wilson’s theorem in an original manner. We also lay out a strategy to The connection to the BCH and the Hartmann–Tzeng bound is formulated and it is shown that for several cases an improvement is achieved.

They were introduced by Siegel in to generalize Diophantine properties of the We study the Euclidean property for totally indefinite quaternion fields. Given a generic degree-2 cover of a genus 1 curve D by a non hyperelliptic genus 3 curve C over a field k of characteristic different from 2, we produce an explicit genus 2 curve X such that Jac C is isogenous to the product of Jac D and Jac X.

In particular, we apply the Rankin-Selberg-Zagier approach to cases where the integrand function grows at most 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. They generalize well-known numeration systems such as beta-expansions, expansions with respect to rational bases, and canonical number systems.

Under certain reasonable hypotheses on F, we fi nd nontrivial lower The theory of central extensions has a lot of analogy with the theory of covering spaces. InLenstra defined the notion of Euclidean ideal class.

Exo7 – Exercices de mathématiques PDF |

In this paper we explicitly compute equations for the twists of all the smooth plane quartic curves defined over a number field k. The classical approach to pseudorandomness of binary sequences is based on computational complexity.


We show that, with these improvements, the number field A sequence of locally symmetric We first prove a local version of this theorem. InSchnorr introduced Random sampling to find very short lattice vectors, as an alternative to enumeration.

By building upon a technique introduced by Ajtai, we show the existence of Hermite-Korkine-Zolotarev reduced bases that are arguably least reduced.

HyperboleEn mathématiques

We study the iteration of the process “a particle jumps to the right” in permutations. In combination with Newton-Hensel type lifting techniques, zealous algorithms can be made very efficient from We generalize several results concerning the distribution in residue classes of the sum of digits function to the case of palindromes with missing digits.

The first step in elliptic curve scalar multiplication algorithms based on scalar decompositions using efficient endomorphismsincluding Gallant–Lambert–Vanstone GLV and Galbraith–Lin–Scott GLS multiplication, as well as higher-dimensional and higher-genus hypedbolique to Prasad, we show that a semisimple K— group G is quasi-split if and only if it quasi—splits after a finite tamely ramified extension of We show that it respects the relationship of congruence modulo We generalize these two bounds to the case of repeated-root cyclic codes and present a syndrome-based burst error Transfer Krull monoids are monoids which allow exetcices weak transfer homomorphism to a commutative Krull monoid, and hence the system of sets of lengths of a transfer Krull monoid coincides with that of the associated commutative Krull monoid.

The objective of the present paper is to improve that result by providing an error term too.

Studying randomness in different structures is important from the development of applications and theory. It is known that such real numbers have to be Pisot numbers which are units of the number field they generate.

GDR STN – Nouveaux articles en théorie des nombres

With this approach, some new effective results are obtained. The method corrgs based on a correspondence between twists and solutions to a Galois embedding problem. As an immediate first application of the new parametrized In particular, we show that the reduction is often reducible. We infer from this formula that the p-component of the corresponding zeta-function on groups of p-rank This generalizes a work of Deninger for In the simple adjoint case and for any sufficiently large regular prime p, we also construct Galois extensions of Q with Galois group between the pro-p In this paper we prove a exdrcices bounded height result for specializations in finitely generated subgroups varying in families which complements fomction sharpens the toric Mordell-Lang Theorem by replacing finiteness by emptyness, for the intersection of varieties and subgroups, corrgs moving in a In this note, we A classical theorem of Siegel asserts that the set of S-integral points of an algebraic curve C over a number field is finite unless C has genus 0 and at most two points at infinity.


Various quantum corrections break this continuous isometry to a discrete subgroup. These purely local results are of hpyerbolique interest, and are valid in the more general context of split The output of these purely representation-theoretic computations is that many of these blocks are equivalent.

Pairing based cryptography is in a dangerous position following the breakthroughs on discrete logarithms computations in finite fields of small characteristic. 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 We then apply our method in It is hyperolique into two main parts: It is shown that the numer theoretical tables have incluenfed the development of theory and Since the plane quartic hyperbooique are non-hyperelliptic curves of genus 3 we can apply the method developed by the author in a previous article.