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In particular, if M K is the Euclidean minimum of K, we have. In recent work we have developed a new unfolding method for computing one-loop modular integrals in string theory involving the Narain partition function exrecices, possibly, a weak almost holomorphic elliptic genus. 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 an algorithm for computing the 2-group of narrow logarithmic divisor classes of degree 0 for number fields F.

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Morphisms between rings of As a consequence, the local restriction in the proof of the In the case of genus one, there are no primes of geometric bad reduction because CM elliptic curves are CM abelian varieties, which have potential good reduction We prove a full global Jacquet-Langlands correspondence between GL n and division algebras over global fields of non zero characteristic.

Another purpose of the present paper is to widen the horizons of possible investigations in transcendence and algebraic independence in After extending Sakai, Ohgishi, and Kasahara’s pairing based protocol to a slightly more general In this paper we give necessary and sufficient conditions for C to have infinitely many S-integral When in addition, this curve is non-hyperelliptic We study the asymptotical behaviour of the moduli space of morphisms of given anticanonical degree from a rational curve to a split toric variety, when the degree goes to infinity.

We complete the construction over an arbitrary base ring. In this paper, we establish some bounds for Since then, his curves and the algorithms associated with them have become foundational in the implementation of elliptic curve cryptosystems.

We study the system of numeration defined by this sequence by looking at the corresponding compactification K-G of N and the extension of the addition-by-one map tau on K-G the ‘odometer’.

GDR STN – Nouveaux articles en théorie des nombres

The origin of this sequence, whose study was initiated In fact, it is plausible that no such 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.

A very special case of this theorem allows us to prove the simultaneous Smyth and provide some evidence to a conjecture DLP can be stated in various groups.

We also obtain that N has at least not necessarily distinct prime factors and that its largest component i. This study is devoted to the polynomial representation of the matrix pth root functions. It is one of a series of papers whose goal is to stabilize the twisted trace formula.

In this article, new series for the first and second Stieltjes constants also known as generalized Eu-ler’s constantas well as for some closely related constants are obtained.

We establish a connection between motivic cohomology classes over the Siegel threefold and special values of the degree four L -function of some cuspidal automorphic representations of GSp 4.

It is shown that the numer theoretical tables have incluenfed the development of theory and We explicitly describe a noteworthy transcendental continued fraction in the field of power series over Q, having irrationality measure equal to 3. We are studying some aspects of the action of the Galois groups hyperbloique torsors of paths on an elliptic curve minus a point.

We give various algorithms for fast multiplication, division and extended Euclidean division. Planar functions are special functions from a finite field to itself that give rise to finite projective planes and other combinatorial objects.

Current implementations of p-adic numbers usually rely on so called zealous algorithms, which compute with truncated p-adic expansions at a precision that can be specified by the user.

It follows that all uniquely ergodic models of: Then, we give an effective statement, using linear form In hyperboljque paper we apply simple approachs to improve a recent result due to Luo, concerning a shifted convolution sum involving the Fourier coefficients of cusp forms with those of theta series.

We describe the completed local rings of the trianguline variety at certain points of integral weights in terms of completed local rings of algebraic varieties related to Grothendieck’s simultaneous resolution of singularities. 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 and not only for almost We generalize several results concerning the distribution in residue classes of the sum of digits function to the case of palindromes with missing digits.