Search

De Moivre est l'auteur de deux livres de mathématiques : The Doctrine of Chances (« La Théorie du hasard ») et Miscellanea Analytica , dans lesquels il pose les fondations des probabilités modernes. Y apparaît pour la première fois la loi normale (associée à la fameuse courbe en cloche) qui aura le succès que l'on connaît. Il est aussi l'auteur d'une formule « magique » associant trigonométrie et nombres imaginaires. Développée par Euler et ses successeurs, cette formule est le premier chaînon de la théorie des fonctions analytiques. Le nom d'Abraham de Moivre apparaît ainsi en terminale des lycées (Théorème de Moivre–Laplace) et en première année de cursus universitaire (formule de Moivre trigonométrique). [ABSTRACT FROM AUTHOR]

Abstract: Let be the kth moment of the number of integers coprime to q in an interval of length h centered on its mean . By comparison with the kth centered moment of the binomial distribution with parameters h and P, for which we show uniformly in k, h and P and where is an absolute constant, we prove the following upper bound where is an absolute constant, uniformly in k, h and q provided that every prime factor of q is greater than or equal to h. [Copyright &y& Elsevier]

Copyright of Mathématiques & Sciences Humaines is the property of Editions du CNRS and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)