Algebraic Theory Of Numbers Am 1 Volume 1
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Author | : Hermann Weyl |
Publisher | : |
Total Pages | : 234 |
Release | : 2016 |
Genre | : Algebraic number theory |
ISBN | : |
Download Algebraic Theory of Numbers. (AM-1), Volume 1 Book in PDF, Epub and Kindle
In this, one of the first books to appear in English on the theory of numbers, the eminent mathematician Hermann Weyl explores fundamental concepts in arithmetic. The book begins with the definitions and properties of algebraic fields, which are relied upon throughout. The theory of divisibility is then discussed, from an axiomatic viewpoint, rather than by the use of ideals. There follows an introduction to p-adic numbers and their uses, which are so important in modern number theory, and the book culminates with an extensive examination of algebraic number fields. Weyl's own modest hope, that the work "will be of some use," has more than been fulfilled, for the book's clarity, succinctness, and importance rank it as a masterpiece of mathematical exposition.
Author | : Hermann Weyl |
Publisher | : Princeton University Press |
Total Pages | : 240 |
Release | : 2016-04-21 |
Genre | : Mathematics |
ISBN | : 140088280X |
Download Algebraic Theory of Numbers. (AM-1), Volume 1 Book in PDF, Epub and Kindle
In this, one of the first books to appear in English on the theory of numbers, the eminent mathematician Hermann Weyl explores fundamental concepts in arithmetic. The book begins with the definitions and properties of algebraic fields, which are relied upon throughout. The theory of divisibility is then discussed, from an axiomatic viewpoint, rather than by the use of ideals. There follows an introduction to p-adic numbers and their uses, which are so important in modern number theory, and the book culminates with an extensive examination of algebraic number fields. Weyl's own modest hope, that the work "will be of some use," has more than been fulfilled, for the book's clarity, succinctness, and importance rank it as a masterpiece of mathematical exposition.
Author | : Paulo Ribenboim |
Publisher | : Springer Science & Business Media |
Total Pages | : 676 |
Release | : 2013-11-11 |
Genre | : Mathematics |
ISBN | : 0387216901 |
Download Classical Theory of Algebraic Numbers Book in PDF, Epub and Kindle
The exposition of the classical theory of algebraic numbers is clear and thorough, and there is a large number of exercises as well as worked out numerical examples. A careful study of this book will provide a solid background to the learning of more recent topics.
Author | : H. P. F. Swinnerton-Dyer |
Publisher | : Cambridge University Press |
Total Pages | : 164 |
Release | : 2001-02-22 |
Genre | : Mathematics |
ISBN | : 9780521004237 |
Download A Brief Guide to Algebraic Number Theory Book in PDF, Epub and Kindle
Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
Author | : Oystein Ore |
Publisher | : Courier Corporation |
Total Pages | : 404 |
Release | : 2012-07-06 |
Genre | : Mathematics |
ISBN | : 0486136434 |
Download Number Theory and Its History Book in PDF, Epub and Kindle
Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.
Author | : Harris Hancock |
Publisher | : |
Total Pages | : 602 |
Release | : 1931 |
Genre | : |
ISBN | : |
Download Foundations of the Theory of Algebraic Numbers. Volume 1: Introduction to the General Theory Book in PDF, Epub and Kindle
Author | : Henry B. Mann |
Publisher | : |
Total Pages | : 178 |
Release | : 2013-03 |
Genre | : |
ISBN | : 9781258639495 |
Download Introduction to Algebraic Number Theory Book in PDF, Epub and Kindle
Author | : Daniel Kriz |
Publisher | : Princeton University Press |
Total Pages | : 280 |
Release | : 2021-11-09 |
Genre | : Mathematics |
ISBN | : 0691216479 |
Download Supersingular P-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas Book in PDF, Epub and Kindle
A groundbreaking contribution to number theory that unifies classical and modern results This book develops a new theory of p-adic modular forms on modular curves, extending Katz's classical theory to the supersingular locus. The main novelty is to move to infinite level and extend coefficients to period sheaves coming from relative p-adic Hodge theory. This makes it possible to trivialize the Hodge bundle on the infinite-level modular curve by a "canonical differential" that restricts to the Katz canonical differential on the ordinary Igusa tower. Daniel Kriz defines generalized p-adic modular forms as sections of relative period sheaves transforming under the Galois group of the modular curve by weight characters. He introduces the fundamental de Rham period, measuring the position of the Hodge filtration in relative de Rham cohomology. This period can be viewed as a counterpart to Scholze's Hodge-Tate period, and the two periods satisfy a Legendre-type relation. Using these periods, Kriz constructs splittings of the Hodge filtration on the infinite-level modular curve, defining p-adic Maass-Shimura operators that act on generalized p-adic modular forms as weight-raising operators. Through analysis of the p-adic properties of these Maass-Shimura operators, he constructs new p-adic L-functions interpolating central critical Rankin-Selberg L-values, giving analogues of the p-adic L-functions of Katz, Bertolini-Darmon-Prasanna, and Liu-Zhang-Zhang for imaginary quadratic fields in which p is inert or ramified. These p-adic L-functions yield new p-adic Waldspurger formulas at special values.
Author | : Andre Weil |
Publisher | : Springer Science & Business Media |
Total Pages | : 335 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642619452 |
Download Basic Number Theory Book in PDF, Epub and Kindle
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
Author | : A. Fröhlich |
Publisher | : Cambridge University Press |
Total Pages | : 376 |
Release | : 1991 |
Genre | : Mathematics |
ISBN | : 9780521438346 |
Download Algebraic Number Theory Book in PDF, Epub and Kindle
This book originates from graduate courses given in Cambridge and London. It provides a brisk, thorough treatment of the foundations of algebraic number theory, and builds on that to introduce more advanced ideas. Throughout, the authors emphasise the systematic development of techniques for the explicit calculation of the basic invariants, such as rings of integers, class groups, and units. Moreover they combine, at each stage of development, theory with explicit computations and applications, and provide motivation in terms of classical number-theoretic problems. A number of special topics are included that can be treated at this level but can usually only be found in research monographs or original papers, for instance: module theory of Dedekind domains; tame and wild ramifications; Gauss series and Gauss periods; binary quadratic forms; and Brauer relations. This is the only textbook at this level which combines clean, modern algebraic techniques together with a substantial arithmetic content. It will be indispensable for all practising and would-be algebraic number theorists.