Download or read book Nombres premiers written by Paulo Ribenboim and published by Presses Universitaires de France - PUF. This book was released on 1994 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Les nombres premiers written by William John Ellison and published by . This book was released on 1975 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sur Le Theoreme Foundamental Des Nombres Premiers written by Alfred Errera and published by . This book was released on 1955 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Catalogue of Scientific Papers 1800 1900 written by Royal Society (Great Britain) and published by . This book was released on 1870 with total page 1022 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Le spectre des surfaces hyperboliques written by Nicolas Bergeron and published by Harlequin. This book was released on 2011 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is an introduction to the spectral theory of the Laplacian on compact or finite area hyperbolic surfaces. For some of these surfaces, called ĺlarithmetic hyperbolic surfacesĺl, the eigenfunctions are of arithmetic nature, and one may use analytic tools as well as powerful methods in number theory to study them. After an introduction to the hyperbolic geometry of surfaces, with a special emphasis on those of arithmetic type, and then an introduction to spectral analytic methods on the Laplace operator on these surfaces, the author develops the analogy between geometry (closed geodesics) and arithmetic (prime numbers) in proving the Selberg trace formula. Along with important number theoretic applications, the author exhibits applications of these tools to the spectral statistics of the Laplacian and the quantum unique ergodicity property. The latter refers to the arithmetic quantum unique ergodicity theorem, recently proved by Elon Lindenstrauss. The fruit of several graduate level courses at Orsay and Jussieu, The Spectrum of Hyperbolic Surfaces allows the reader to review an array of classical results and then to be led towards very active areas in modern mathematics.
Download or read book The Collected Mathematical Papers of James Joseph Sylvester written by James Joseph Sylvester and published by . This book was released on 1912 with total page 799 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Catalogue of Scientific Papers written by Royal Society (Great Britain) and published by . This book was released on 1870 with total page 1022 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Les nombres premiers written by Emile Borel and published by . This book was released on 1953 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Joseph Liouville 1809 1882 written by Jesper Lützen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 893 pages. Available in PDF, EPUB and Kindle. Book excerpt: This scientific biography of the mathematician Joseph Liouville is divided into two parts. The first part is a chronological account of Liouville's career including a description of the institutions he worked in, his relations with his teachers, colleagues and students, and the historical context of his works. It portrays the French scientific community in a period when Germany and England had surpassed France as the leading nations in mathematics and physics. The second part of the book gives a detailed analysis of Liouville's major contributions to mathematics and mechanics. The gradual development of Liouville's ideas, as reflected in his publications and notebooks, are related to the works of his predecessors and his contemporaries as well as to later developments in the field. On the basis of Liouville's unpublished notes the book reconstructs Liouville's hitherto unknown theories of stability of rotating masses of fluid, potential theory, Galois theory and electrodynamics. It also incorporates valuable added information from Liouville's notes regarding his works on differentiation of arbitrary order, integration in finite terms, Sturm-Liouville theory, transcendental numbers, doubly periodic functions, geometry and mechanics.
Download or read book Catalogue of Scientific Papers 1800 1900 ser 1 1800 1863 written by Royal Society (Great Britain) and published by . This book was released on 1870 with total page 1028 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Number Theory written by Jean-Marie De Koninck and published by Walter de Gruyter. This book was released on 1989 with total page 1038 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monumental proceedings (very handsomely produced) of a major international conference. The book contains 74 refereed articles which, apart from a few survey papers of peculiar interest, are mostly research papers (63 in English, 11 in French). The topics covered reflect the full diversity of the current trends and activities in modern number theory: elementary, algebraic and analytic number theory; constructive (computational) number theory; elliptic curves and modular forms; arithmetical geometry; transcendence; quadratic forms; coding theory. (NW) Annotation copyrighted by Book News, Inc., Portland, OR
Download or read book Book Catalogue written by and published by . This book was released on 1852 with total page 1010 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Selecta Diophantine problems and polynomials written by Andrzej Schinzel and published by European Mathematical Society. This book was released on 2007 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cryptographie principes et mises en uvre 2 me dition revue et augment e written by BARTHELEMY Pierre and published by Lavoisier. This book was released on 2012-04-16 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quels sont les enjeux de la cryptographie moderne ? Quels sont ses objets, son langage ? Quelles sont les solutions actuelles aux problèmes de confidentialité, d'authentification et d'anonymat ? Quel degré de confiance peut-on accorder à ces solutions ? Cette seconde édition, enrichie et mise à jour, propose un panorama des outils et procédés de la cryptographie. Après avoir présenté et analysé les méthodes, cet ouvrage offre une description précise des techniques mathématiques indispensables et des principales primitives cryptographiques. Les fonctionnalités de base comme le chiffrement, la signature ou l'authentification, sont étudiées dans le cadre de la cryptographie à clé publique ou secrète. Cryptographie analyse également l'interaction entre ces notions ainsi que leurs mises en oeuvre dans des protocoles généraux et dans des applications concrètes. Il s'intéresse aux attaques contre les systèmes cryptographiques y compris celles par canaux cachés et par injection de fautes. Il aborde le domaine désormais indispensable des preuves de sécurité.
Download or read book The Grothendieck Festschrift Volume III written by Pierre Cartier and published by Springer. This book was released on 2007-10-23 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: This three-volume work contains articles collected on the occasion of Alexander Grothendieck’s sixtieth birthday and originally published in 1990. The articles were offered as a tribute to one of the world’s greatest living mathematicians. Many of the groundbreaking contributions in these volumes contain material that is now considered foundational to the subject. Topics addressed by these top-notch contributors match the breadth of Grothendieck’s own interests, including: functional analysis, algebraic geometry, algebraic topology, number theory, representation theory, K-theory, category theory, and homological algebra.
