Download or read book Initiation la th orie analytique des nombres premiers written by André Blanchard and published by . This book was released on 1969 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Initiation la th orie analytique des nombres premiers written by Blanchard and published by . This book was released on 1965 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction la th orie analytique et probabiliste des nombres written by Gérald Tenenbaum and published by . This book was released on 1990 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Un cours de th orie analytique des nombres written by Emmanuel Kowalski and published by SMF. This book was released on 2004 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ce livre est une introduction à la théorie multiplicative des nombres premiers. Il est divisé approximativement en deux parties. La première introduit les méthodes classiques basées sur les propriétés analytiques des séries de Dirichlet, menant aux résultats fondamentaux tournant autour du théorème des nombres premiers dans les progressions arithmétiques. La seconde expose des méthodes faisant partie des thèmes de recherche les plus actuels pour démontrer un théorème de Duke, Friedlander et Iwaniec sur l'équirépartition des racines d'un polynôme quadratique modulo les nombres premiers (ce résultat sert de fil rouge durant tout le livre). Les deux points essentiels sont des résultats de crible non limités aux entiers " presque premiers ", et l'exploitation des résultats de la théorie spectrale des formes automorphes.
Download or read book Le th or me des nombres premiers written by Michel Balazard and published by . This book was released on 2016-09-08 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Le présent fascicule de la collection Nano est une introduction à l'application des méthodes de l'analyse réelle à l'étude de la répartition des nombres premiers. Le texte a pour fil conducteur l'énoncé emblématique de la théorie analytique des nombres : le théorème des nombres premiers, qui affirme que le nombre de nombres premiers inférieurs ou égaux à x est asymptotiquement équivalent à x/ln(x), quand x tend vers l'infini. Autrement dit, l'écart moyen entre les N premiers nombres premiers est de l'ordre de 1n(N). Cet énoncé et des progrès vers sa démonstration furent l'oeuvre de Legendre, Gauss, Lejeune Dirichlet et Tchebychev. Ce sont Hadamard et la Vallée Poussin (1896), qui donnèrent finalement, et de façon indépendante, une démonstration complète, mettant à profit les idées géniales de Riemann sur l'application de la théorie des fonctions d'une variable complexe à l'étude des nombres premiers, en rapport notamment avec ce que la postérité appela la fonction zêta de Riemann. Ces idées étaient si originales, et le résultat si brillant, que peu nombreux furent ceux qui se décidèrent à chercher une autre voie, élémentaire, vers la démonstration. Celle-ci ne fut finalement trouvée que plus d'un demi-siècle plus tard, par Erdös et Selberg (1949). Leurs idées renouvelèrent profondément ce domaine de recherches, et l'ambition de Michel Balazard a été en rédigeant ce livre de les présenter comme partie essentielle de la théorie générale des fonctions arithmétiques. Le texte, qui ne manque pas de poésie, parut d'abord en russe comme la version développée d'une série de quatre cours donnés en 2009 à l'école d'été "Mathématiques Contemporaines" de Dubna (au nord de Moscou) et destinés aux élèves des lycées et universités. Le contenu a été également l'objet de deux exposés dans le cadre du séminaire pour étudiants "Mathematic Park", à Paris, en 2010. La présente version est plus approfondie, mais reste certainement accessible à partir des connaissances acquises dans les deux premières années d'université. Les soixante-cinq exercices permettent, avec leurs solutions, d'assimiler activement les notions et techniques introduites.
Download or read book Introduction to Analytic and Probabilistic Number Theory written by Gérald Tenenbaum and published by American Mathematical Society. This book was released on 2024-06-26 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self contained, thorough introduction to the analytic and probabilistic methods of number theory. The prerequisites being reduced to classical contents of undergraduate courses, it offers to students and young researchers a systematic and consistent account on the subject. It is also a convenient tool for professional mathematicians, who may use it for basic references concerning many fundamental topics. Deliberately placing the methods before the results, the book will be of use beyond the particular material addressed directly. Each chapter is complemented with bibliographic notes, useful for descriptions of alternative viewpoints, and detailed exercises, often leading to research problems. This third edition of a text that has become classical offers a renewed and considerably enhanced content, being expanded by more than 50 percent. Important new developments are included, along with original points of view on many essential branches of arithmetic and an accurate perspective on up-to-date bibliography. The author has made important contributions to number theory and his mastery of the material is reflected in the exposition, which is lucid, elegant, and accurate. —Mathematical Reviews
Download or read book Introduction la th orie analytique et probabiliste des nombres written by Gérald Tenenbaum and published by Dunod. This book was released on 2022-01-05 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solide initiation aux méthodes analytiques et probabilistes de l’arithmétique, ce livre constitue une base de référence autonome. Ne s’appuyant que sur les connaissances traditionnellement enseignées dans les deux premiers cycles universitaires, il fournit aux étudiants (notamment les candidats à l’agrégation et/ou au CAPES de mathématiques) une présentation systématique du domaine. L’ouvrage constitue également un précieux instrument de travail pour les chercheurs, jeunes ou confirmés, en décrivant l’état de l’art pour les questions fondamentales de la discipline. Centrée sur les méthodes plus que sur les résultats, l'approche générale donne immédiatement accès à des développements dépassant largement le cadre strict de la théorie des nombres. Les chapitres sont complétés par des notes détaillées, ouvrant sur la bibliographie la plus récente, et par plus de 300 exercices de niveaux variés. Cette cinquième édition d’un texte devenu classique, inclus dans la bibliothèque de l’agrégation depuis de nombreuses années, offre un contenu renouvelé et enrichi. Elle s’appuie sur d’importants développements inédits, et porte des points de vue originaux sur plusieurs branches essentielles de l’arithmétique.
Download or read book Groupe d tude en th orie analytique des nombres written by Groupe d'étude en théorie analytique des nombres (Paris). and published by . This book was released on 1985 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Course in Arithmetic written by J-P. Serre and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is divided into two parts. The first one is purely algebraic. Its objective is the classification of quadratic forms over the field of rational numbers (Hasse-Minkowski theorem). It is achieved in Chapter IV. The first three chapters contain some preliminaries: quadratic reciprocity law, p-adic fields, Hilbert symbols. Chapter V applies the preceding results to integral quadratic forms of discriminant ± I. These forms occur in various questions: modular functions, differential topology, finite groups. The second part (Chapters VI and VII) uses "analytic" methods (holomor phic functions). Chapter VI gives the proof of the "theorem on arithmetic progressions" due to Dirichlet; this theorem is used at a critical point in the first part (Chapter Ill, no. 2.2). Chapter VII deals with modular forms, and in particular, with theta functions. Some of the quadratic forms of Chapter V reappear here. The two parts correspond to lectures given in 1962 and 1964 to second year students at the Ecole Normale Superieure. A redaction of these lectures in the form of duplicated notes, was made by J.-J. Sansuc (Chapters I-IV) and J.-P. Ramis and G. Ruget (Chapters VI-VII). They were very useful to me; I extend here my gratitude to their authors.
Download or read book Introduction la th orie des nombres written by V.-A. Le Besgue and published by . This book was released on 1862 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Les nombres premiers entre l ordre et le chaos 2e d written by Gérald Tenenbaum and published by Dunod. This book was released on 2014-01-08 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quoi de plus fascinant que les nombres premiers ? Depuis la plus haute Antiquité, leur suite infinie passionne mathématiciens, philosophes et profanes : régulière puisqu’arithmétique, et cependant d’allure chaotique et aléatoire, elle constitue une intarissable source de défis pour l’esprit humain. La recherche est plus active que jamais dans ce domaine de la théorie des nombres : en témoignent de récentes et prestigieuses découvertes, comme la spectaculaire avancée sur le problème millénaire des nombres premiers jumeaux. Cette nouvelle édition actualisée invite le lecteur à une promenade initiatique autour du problème de la répartition des nombres premiers parmi les nombres entiers. Historique et méthodologique, ce texte constitue une concise mais solide introduction aux techniques actuelles de la théorie analytique des nombres premiers.
Download or read book Cours de th orie analytique des nombres written by Gérald Tenenbaum and published by . This book was released on 1979 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Initiation la th orie des nombres written by Øystein Ore and published by . This book was released on 1970 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Exercises in Number Theory written by D.P. Parent and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: After an eclipse of some 50 years, Number Theory, that is to say the study of the properties of the integers, has regained in France a vitality worthy of its distinguished past. More 'and more researchers have been attracted by problems which, though it is possible to express in simple statements, whose solutions require all their ingenuity and talent. In so doing, their work enriches the whole of mathematics with new and fertile methods. To be in a position to tackle these problems, it is neces sary to be familiar with many specific aspects of number theory. These are very different from those encountered in analysis or geometry. The necessary know-how can only be acquired by study ing and solving numerous problems. Now it is very easy to form ulate problems whose solutions, while sometimes obvious, more often go beyond current methods. Moreover, there is no doubt that, even more than in other disciplines, in mathematics one must have exercises available whose solutions are accessible. This is the objective realised by this work. It is the collab orative work of several successful young number theorists. They have drawn these exercises from their own work, from the work of their associated research groups as well as from published work.
Download or read book The Development of Prime Number Theory written by Wladyslaw Narkiewicz and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. People were already interested in prime numbers in ancient times, and the first result concerning the distribution of primes appears in Euclid's Elemen ta, where we find a proof of their infinitude, now regarded as canonical. One feels that Euclid's argument has its place in The Book, often quoted by the late Paul ErdOs, where the ultimate forms of mathematical arguments are preserved. Proofs of most other results on prime number distribution seem to be still far away from their optimal form and the aim of this book is to present the development of methods with which such problems were attacked in the course of time. This is not a historical book since we refrain from giving biographical details of the people who have played a role in this development and we do not discuss the questions concerning why each particular person became in terested in primes, because, usually, exact answers to them are impossible to obtain. Our idea is to present the development of the theory of the distribu tion of prime numbers in the period starting in antiquity and concluding at the end of the first decade of the 20th century. We shall also present some later developments, mostly in short comments, although the reader will find certain exceptions to that rule. The period of the last 80 years was full of new ideas (we mention only the applications of trigonometrical sums or the advent of various sieve methods) and certainly demands a separate book.
Download or read book Rational Number Theory in the 20th Century written by Władysław Narkiewicz and published by Springer Science & Business Media. This book was released on 2011-09-02 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last one hundred years have seen many important achievements in the classical part of number theory. After the proof of the Prime Number Theorem in 1896, a quick development of analytical tools led to the invention of various new methods, like Brun's sieve method and the circle method of Hardy, Littlewood and Ramanujan; developments in topics such as prime and additive number theory, and the solution of Fermat’s problem. Rational Number Theory in the 20th Century: From PNT to FLT offers a short survey of 20th century developments in classical number theory, documenting between the proof of the Prime Number Theorem and the proof of Fermat's Last Theorem. The focus lays upon the part of number theory that deals with properties of integers and rational numbers. Chapters are divided into five time periods, which are then further divided into subject areas. With the introduction of each new topic, developments are followed through to the present day. This book will appeal to graduate researchers and student in number theory, however the presentation of main results without technicalities will make this accessible to anyone with an interest in the area.
