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Automorphic forms and even unimodular lattices : Kneser neighbors of niemeier lattices
This book includes a self-contained approach of the general theory of quadratic forms and integral Euclidean lattices.It explains how the new advances in the Langlands program mentioned above pave the way for a solution. This study proves to be very rich, leading us to classical themes such as theta series, Siegel modular forms, the triality principle, L-functions and congruences between Galois representations.
Binary Quadratic Forms: An Algorithmic Approach
This book deals with algorithmic problems concerning binary quadratic forms 2 2 f(X,Y)= aX +bXY +cY with integer coe?cients a, b, c, the mathem- ical theories that permit the solution of these problems, and applications to cryptography.
Algèbre, Chapitre 9 = Algebra, Chapter 9
Sesquilinear and quadratic forms : The Mathematics Elements of Nicolas BOURBAKI aim to provide a rigorous, systematic presentation without prerequisites of mathematics from their foundations. This ninth chapter of the Book of Algebra, the second Book of the treatise, is devoted to quadratic, symplectic or Hermitian forms and to associated groups.
Algebra : Fields with structure, algebras and advanced topics
The present textbook is a lively, problem-oriented and carefully written introduction to classical modern algebra. The author leads the reader through interesting subject matter, while assuming only the background provided by a first course in linear algebra. The first volume focuses on field extensions. Galois theory and its applications are treated more thoroughly than in most texts. It also covers basic applications to number theory, ring extensions and algebraic geometry. The main focus of the second volume is on additional structure of fields and related topics. Much material not usually covered in textbooks appears here, including real fields and quadratic forms, the Tsen rank of a field, the calculus of Witt vectors, the Schur group of a field, and local class field theory.
