From the reviews: "L.R. Shafarevich showed me the first edition […] and said that this book will be from now on the book about class field theory. In fact it is by far the most complete treatment of the main theorems of algebraic number theory, including function fields over finite constant fields, that appeared in book form." Zentralblatt MATH

Basic number theory (Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen)

Science & Math

André Weil

Mathematics

Springer, Verlag

From the reviews: "L.R. Shafarevich showed me the first edition [â€¦] and said that this book will be from now on the book about class field theory. In fact it is by far the most complete treatment of the main theorems of algebraic number theory, including function fields over finite constant fields, that appeared in book form." Zentralblatt MATH

Basic Number Theory (Grundlehren Der Mathematischen Wissenschaften Volume 144)

Springer

certain rational varieties (spaces of straight lines, of conics, etc. ), whereas we shall emphasize the geometry on an arbitrary variety, or at least on a variety without multiple points. The theory of intersection-multiplicities, however, occupies such a centrat position among the topics which constitute the founda tions of algebraic geometry, that a complete treatment of it necessarily supplies the tools by which many other such topics can be dealt with. In deciding be tween alternative methods of proof for the theorems in this book, consistency, and the possibility of applying these methods to further problems, have been the main considerations; for instance, one will find here all that is needed for the proof of Bertini's theorems, for a detailed ideal-theoretic study (by geometric means) of the quotient-ring of a simple point, for the elementary part of the theory of linear series, and for a rigorous definition of the various concepts of equivalence. In consequence, the author has deliberately avoided a few short cuts; this is not to say that there may not be many more which he did not notice, and which our readers, it is hoped, may yet discover. Our method of exposition will be dogmatic and unhistorical throughout, formal proofs, without references, being given at every step.

Oeuvres Scientifiques / Collected Papers: Volume 1 (1926-1951). Volume 2 (1951-1964). Volume 3 (1964-1978) (French, English, German Edition) (French, English and German Edition)

History

Europe

This book presents a historical overview of number theory. It examines texts that span some thirty-six centuries of arithmetical work, from an Old Babylonian tablet to Legendre’s Essai sur la Théorie des Nombres, written in 1798. Coverage employs a historical approach in the analysis of problems and evolving methods of number theory and their significance within mathematics. The book also takes the reader into the workshops of four major authors of modern number theory: Fermat, Euler, Lagrange and Legendre and presents a detailed and critical examination of their work.

Number Theory: An approach through history From Hammurapi to Legendre

History & Philosophy

Birkhäuser Boston

Basic Number Theory (Grundlehren der mathematischen Wissenschaften)

From the reviews: "L.R. Shafarevich showed me the first edition […] and said that this book will be from now on the book about class field theory. In fact it is by far the most complete treatment of the main theorems of algebraic number theory, including function fields over finite constant fields, that appeared in book form." Zentralblatt MATH

Drawn from the Foreword: (...) On the other hand, since much of the material in this volume seems suitable for inclusion in elementary courses, it may not be superfluous to point out that it is almost entirely self-contained. Even the basic facts about trigonometric functions are treated ab initio in Ch. II, according to Eisenstein's method. It would have been both logical and convenient to treat the gamma -function similarly in Ch. VII; for the sake of brevity, this has not been done, and a knowledge of some elementary properties of T(s) has been assumed. One further prerequisite in Part II is Dirichlet's theorem on Fourier series, together with the method of Poisson summation which is only a special case of that theorem; in the case under consideration (essentially no more than the transformation formula for the theta-function) this presupposes the calculation of some classical integrals. (...) As to the final chapter, it concerns applications to number theory (...).

Elliptic Functions according to Eisenstein and Kronecker (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge)

From the reviews: "…All of Weil’s works except for books and lecture notes are compiled here, in strict chronological order for easy reference. But the value … goes beyond the convenience of easy reference and accessibility. In the first place, these volumes contain several essays, letters, and addresses which were either published in obscure places (…) or not published at all.  Even more valuable are the lengthy commentaries on many of the articles, written by Weil himself. These remarks serve as a guide, helping the reader place the papers in their proper context. Moreover, we have the rare opportunity of seeing a great mathematician in his later life reflecting on the development of his ideas and those of his contemporaries at various stages of his career. The sheer number of mathematical papers of fundamental significance would earn Weil’s Collected Papers a place in the library of a mathematician with an interest in number theory, algebraic geometry, representations theory, or related areas. The additional import of the mathematical history and culture in these volumes makes them even more essential." Neal Koblitz in Mathematical Reviews  "…André Weil’s mathematical work has deeply influenced the mathematics of the twentieth century and the monumental (...) "Collected papers" emphasize this influence." O. Fomenko in Zentralblatt der Mathematik

Oeuvres Scientifiques - Collected Papers II: 1951 - 1964 (English, French and German Edition)

From the reviews"All of Weil’s works except for books and lecture notes are compiled here, in strict chronological order for easy reference.But the value … goes beyond the convenience of easy reference and accessibility. In the first place, these volumes contain several essays, letters, and addresses which were either published in obscure places (…) or not published at all. Even more valuable are the lengthy commentaries on many of the articles, written by Weil himself. These remarks serve as a guide, helping the reader place the papers in their proper context. Moreover, we have the rare opportunity of seeing a great mathematician in his later life reflecting on the development of his ideas and those of his contemporaries at various stages of his career.The sheer number of mathematical papers of fundamental significance would earn Weil’s Collected Papers a place in the library of a mathematician with an interest in number theory, algebraic geometry, representations theory, or related areas. The additional import of the mathematical history and culture in these volumes makes them even more essential." Neal Koblitz in Mathematical Reviews"André Weil’s mathematical work has deeply influenced the mathematics of the twentieth century and the monumental (...) "Collected papers" emphasize this influence." O. Fomenko in Zentralblatt der Mathematik

Oeuvres Scientifiques - Collected Papers III: 1964-1978 (English, French and German Edition)

See the best price to sell, buy, or rent books by André Weil. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by André Weil

See the best price to sell, buy, or rent books by André Weil. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Basic number theory (Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen)

Basic Number Theory (Grundlehren Der Mathematischen Wissenschaften Volume 144)

Oeuvres Scientifiques / Collected Papers: Volume 1 (1926-1951). Volume 2 (1951-1964). Volume 3 (1964-1978) (French, English, German Edition) (French, English and German Edition)

Number Theory: An approach through history From Hammurapi to Legendre

Basic Number Theory (Grundlehren der mathematischen Wissenschaften)

Basic Number Theory (Grundlehren Der Mathematischen Wissenschaften Volume 144)

Basic Number Theory (Grundlehren der mathematischen Wissenschaften)

Elliptic Functions according to Eisenstein and Kronecker (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge)

Oeuvres Scientifiques - Collected Papers II: 1951 - 1964 (English, French and German Edition)

Oeuvres Scientifiques - Collected Papers III: 1964-1978 (English, French and German Edition)