Download or read book The Explicit Construction of Ring Class Fields with Applications to Quadratic Forms written by Howard Pzena and published by . This book was released on 1983 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to the Construction of Class Fields written by Harvey Cohn and published by Courier Corporation. This book was released on 1994-01-01 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: A broad introduction to quadratic forms, modular functions, interpretation by rings and ideals, class fields by radicals and more. 1985 ed.
Download or read book Faithfully Quadratic Rings written by M. Dickmann and published by American Mathematical Soc.. This book was released on 2015-10-27 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph the authors extend the classical algebraic theory of quadratic forms over fields to diagonal quadratic forms with invertible entries over broad classes of commutative, unitary rings where is not a sum of squares and is invertible. They accomplish this by: (1) Extending the classical notion of matrix isometry of forms to a suitable notion of -isometry, where is a preorder of the given ring, , or . (2) Introducing in this context three axioms expressing simple properties of (value) representation of elements of the ring by quadratic forms, well-known to hold in the field case.
Download or read book Lectures On Finite Fields And Galois Rings written by Zhe-xian Wan and published by World Scientific Publishing Company. This book was released on 2003-08-12 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook for graduate and upper level undergraduate students in mathematics, computer science, communication engineering and other fields. The explicit construction of finite fields and the computation in finite fields are emphasised. In particular, the construction of irreducible polynomials and the normal basis of finite fields are included. The essentials of Galois rings are also presented. This invaluable book has been written in a friendly style, so that lecturers can easily use it as a text and students can use it for self-study. A great number of exercises have been incorporated.
Download or read book Lectures on Finite Fields and Galois Rings written by Zhe-Xian Wan and published by World Scientific. This book was released on 2003 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook for graduate and upper level undergraduate students in mathematics, computer science, communication engineering and other fields. The explicit construction of finite fields and the computation in finite fields are emphasised. In particular, the construction of irreducible polynomials and the normal basis of finite fields are included. The essentials of Galois rings are also presented. This invaluable book has been written in a friendly style, so that lecturers can easily use it as a text and students can use it for self-study. A great number of exercises have been incorporated.
Download or read book Finite Fields And Galois Rings written by Zhe-xian Wan and published by World Scientific Publishing Company. This book was released on 2011-09-13 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: A large portion of the book can be used as a textbook for graduate and upper level undergraduate students in mathematics, communication engineering, computer science and other fields. The remaining part can be used as references for specialists. Explicit construction and computation of finite fields are emphasized. In particular, the construction of irreducible polynomials and normal basis of finite field is included. A detailed treatment of optimal normal basis and Galoi's rings is included. It is the first time that the galois rings are in book form.
Download or read book Explicit construction of the Hilbert class fields of imaginary quadratic fields by integer lattice reduction written by Erich Kaltofen and published by . This book was released on 1989 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on Formally Real Fields written by A. Prestel and published by Lecture Notes in Mathematics. This book was released on 1984-11 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Absolute values and their completions - like the p-adic number fields- play an important role in number theory. Krull's generalization of absolute values to valuations made applications in other branches of mathematics, such as algebraic geometry, possible. In valuation theory, the notion of a completion has to be replaced by that of the so-called Henselization. In this book, the theory of valuations as well as of Henselizations is developed. The presentation is based on the knowledge aquired in a standard graduate course in algebra. The last chapter presents three applications of the general theory -as to Artin's Conjecture on the p-adic number fields- that could not be obtained by the use of absolute values only.
Download or read book The Algebraic and Geometric Theory of Quadratic Forms written by Richard S. Elman and published by American Mathematical Soc.. This book was released on 2008-07-15 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive study of the algebraic theory of quadratic forms, from classical theory to recent developments, including results and proofs that have never been published. The book is written from the viewpoint of algebraic geometry and includes the theory of quadratic forms over fields of characteristic two, with proofs that are characteristic independent whenever possible. For some results both classical and geometric proofs are given. Part I includes classical algebraic theory of quadratic and bilinear forms and answers many questions that have been raised in the early stages of the development of the theory. Assuming only a basic course in algebraic geometry, Part II presents the necessary additional topics from algebraic geometry including the theory of Chow groups, Chow motives, and Steenrod operations. These topics are used in Part III to develop a modern geometric theory of quadratic forms.
Download or read book Quadratic Forms and Their Applications written by Eva Bayer-Fluckiger and published by American Mathematical Soc.. This book was released on 2000 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume outlines the proceedings of the conference on "Quadratic Forms and Their Applications" held at University College Dublin. It includes survey articles and research papers ranging from applications in topology and geometry to the algebraic theory of quadratic forms and its history. Various aspects of the use of quadratic forms in algebra, analysis, topology, geometry, and number theory are addressed. Special features include the first published proof of the Conway-Schneeberger Fifteen Theorem on integer-valued quadratic forms and the first English-language biography of Ernst Witt, founder of the theory of quadratic forms.
Download or read book Abstracts of Papers Presented to the American Mathematical Society written by American Mathematical Society and published by . This book was released on 2001 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Algebraic Theory of Quadratic Forms written by Tsit-Yuen Lam and published by . This book was released on 1973 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Classical Invitation to Algebraic Numbers and Class Fields written by Harvey Cohn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Artin's 1932 Göttingen Lectures on Class Field Theory" and "Connections between Algebrac Number Theory and Integral Matrices"
Download or read book Complex Multiplication written by Reinhard Schertz and published by Cambridge University Press. This book was released on 2010-04-29 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a self-contained 2010 account of the state of the art in classical complex multiplication that includes recent results on rings of integers and applications to cryptography using elliptic curves. The author is exhaustive in his treatment, giving a thorough development of the theory of elliptic functions, modular functions and quadratic number fields and providing a concise summary of the results from class field theory. The main results are accompanied by numerical examples, equipping any reader with all the tools and formulas they need. Topics covered include: the construction of class fields over quadratic imaginary number fields by singular values of the modular invariant j and Weber's tau-function; explicit construction of rings of integers in ray class fields and Galois module structure; the construction of cryptographically relevant elliptic curves over finite fields; proof of Berwick's congruences using division values of the Weierstrass p-function; relations between elliptic units and class numbers.
Download or read book Primes of the Form x2 ny2 written by David A. Cox and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern number theory began with the work of Euler and Gauss to understand and extend the many unsolved questions left behind by Fermat. In the course of their investigations, they uncovered new phenomena in need of explanation, which over time led to the discovery of field theory and its intimate connection with complex multiplication. While most texts concentrate on only the elementary or advanced aspects of this story, Primes of the Form x2 + ny2 begins with Fermat and explains how his work ultimately gave birth to quadratic reciprocity and the genus theory of quadratic forms. Further, the book shows how the results of Euler and Gauss can be fully understood only in the context of class field theory. Finally, in order to bring class field theory down to earth, the book explores some of the magnificent formulas of complex multiplication. The central theme of the book is the story of which primes p can be expressed in the form x2 + ny2. An incomplete answer is given using quadratic forms. A better though abstract answer comes from class field theory, and finally, a concrete answer is provided by complex multiplication. Along the way, the reader is introduced to some wonderful number theory. Numerous exercises and examples are included. The book is written to be enjoyed by readers with modest mathematical backgrounds. Chapter 1 uses basic number theory and abstract algebra, while chapters 2 and 3 require Galois theory and complex analysis, respectively.
Download or read book Weil s Conjecture for Function Fields written by Dennis Gaitsgory and published by Princeton University Press. This book was released on 2019-02-19 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: A central concern of number theory is the study of local-to-global principles, which describe the behavior of a global field K in terms of the behavior of various completions of K. This book looks at a specific example of a local-to-global principle: Weil’s conjecture on the Tamagawa number of a semisimple algebraic group G over K. In the case where K is the function field of an algebraic curve X, this conjecture counts the number of G-bundles on X (global information) in terms of the reduction of G at the points of X (local information). The goal of this book is to give a conceptual proof of Weil’s conjecture, based on the geometry of the moduli stack of G-bundles. Inspired by ideas from algebraic topology, it introduces a theory of factorization homology in the setting l-adic sheaves. Using this theory, Dennis Gaitsgory and Jacob Lurie articulate a different local-to-global principle: a product formula that expresses the cohomology of the moduli stack of G-bundles (a global object) as a tensor product of local factors. Using a version of the Grothendieck-Lefschetz trace formula, Gaitsgory and Lurie show that this product formula implies Weil’s conjecture. The proof of the product formula will appear in a sequel volume.
Download or read book Comprehensive Dissertation Index written by and published by . This book was released on 1989 with total page 1016 pages. Available in PDF, EPUB and Kindle. Book excerpt:
