Exposé des principes élémentaires de la théorie des déterminants, à l'usage des élèves de mathématiques spéciales
Expressing a number as the sum of two coprime squares.
We use hyperbolic geometry to study the limiting behavior of the average number of ways of expressing a number as the sum of two coprime squares. An alternative viewpoint using analytic number theory is also given.
Expressing rationals as a sum of a small number of unit fractions
Expression du produit des coefficients du binôme
Expression of real numbers with the help of infinite series
Extended automorphic forms on the upper half plane.
Extended Bell and Stirling numbers from hypergeometric exponentiation.
Extended Euclidean Algorithm and CRT Algorithm
In this article we formalize some number theoretical algorithms, Euclidean Algorithm and Extended Euclidean Algorithm [9]. Besides the a gcd b, Extended Euclidean Algorithm can calculate a pair of two integers (x, y) that holds ax + by = a gcd b. In addition, we formalize an algorithm that can compute a solution of the Chinese remainder theorem by using Extended Euclidean Algorithm. Our aim is to support the implementation of number theoretic tools. Our formalization of those algorithms is based...
Extended Fibonacci numbers and polynomials with probability applications.
Extended GCD and Hermite normal form algorithms via lattice basis reduction.
Extending a recent result of Santos on partitions into odd parts.
Extension aux nombres premiers complexes des théorèmes de M. Tchebicheff
Extension du théorème de Fermat sur les nombres polygones
Extension d'un théorème de Pólya-Cantor à des séries rationnelles en variables non commutatives
Extension of analytic number theory and the theory of regularized harmonic series from Dirichlet series to Bessel series.
Extension of classical sequences to negative integers
We give a method to extend Bell exponential polynomials to negative indices. This generalizes many results of this type such as the extension to negative indices of Stirling numbers or of Bernoulli numbers.
Extension of Estermann’s theorem to Euler products associated to a multivariate polynomial
Given a multivariate polynomial with integral coefficients verifying an hypothesis of analytic regularity (and satisfying ), we determine the maximal domain of meromorphy of the Euler product and the natural boundary is precisely described when it exists. In this way we extend a well known result for one variable polynomials due to Estermann from 1928. As an application, we calculate the natural boundary of the multivariate Euler products associated to a family of toric varieties.
Extension of semiclean rings
This paper aims at the study of the notions of periodic, UU and semiclean properties in various context of commutative rings such as trivial ring extensions, amalgamations and pullbacks. The results obtained provide new original classes of rings subject to various ring theoretic properties.
Extensions à points de ramification donnés (en russe)
Extensions à points de ramification donnés (résumé français)