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On The Class Number Of Abelian Number Fields
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Book Synopsis On the Class Number of Abelian Number Fields by : Helmut Hasse
Download or read book On the Class Number of Abelian Number Fields written by Helmut Hasse and published by Springer. This book was released on 2019-04-23 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this translation, the classic monograph Über die Klassenzahl abelscher Zahlkörper by Helmut Hasse is now available in English for the first time. The book addresses three main topics: class number formulas for abelian number fields; expressions of the class number of real abelian number fields by the index of the subgroup generated by cyclotomic units; and the Hasse unit index of imaginary abelian number fields, the integrality of the relative class number formula, and the class number parity. Additionally, the book includes reprints of works by Ken-ichi Yoshino and Mikihito Hirabayashi, which extend the tables of Hasse unit indices and the relative class numbers to imaginary abelian number fields with conductor up to 100. The text provides systematic and practical methods for deriving class number formulas, determining the unit index and calculating the class number of abelian number fields. A wealth of illustrative examples, together with corrections and remarks on the original work, make this translation a valuable resource for today’s students of and researchers in number theory.
Book Synopsis The Genus Fields of Algebraic Number Fields by : M. Ishida
Download or read book The Genus Fields of Algebraic Number Fields written by M. Ishida and published by Springer. This book was released on 2006-12-08 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: a
Book Synopsis Normal Bases in Class Fields Over Real Abelian Number Fields by : Stephen J. Carlson
Download or read book Normal Bases in Class Fields Over Real Abelian Number Fields written by Stephen J. Carlson and published by . This book was released on 1998 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quadratic Number Fields by : Franz Lemmermeyer
Download or read book Quadratic Number Fields written by Franz Lemmermeyer and published by Springer Nature. This book was released on 2021-09-18 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate textbook provides an elegant introduction to the arithmetic of quadratic number fields, including many topics not usually covered in books at this level. Quadratic fields offer an introduction to algebraic number theory and some of its central objects: rings of integers, the unit group, ideals and the ideal class group. This textbook provides solid grounding for further study by placing the subject within the greater context of modern algebraic number theory. Going beyond what is usually covered at this level, the book introduces the notion of modularity in the context of quadratic reciprocity, explores the close links between number theory and geometry via Pell conics, and presents applications to Diophantine equations such as the Fermat and Catalan equations as well as elliptic curves. Throughout, the book contains extensive historical comments, numerous exercises (with solutions), and pointers to further study. Assuming a moderate background in elementary number theory and abstract algebra, Quadratic Number Fields offers an engaging first course in algebraic number theory, suitable for upper undergraduate students.
Book Synopsis Algebraic Number Fields by : Gerald J. Janusz
Download or read book Algebraic Number Fields written by Gerald J. Janusz and published by American Mathematical Soc.. This book was released on 1996 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents the basic information about finite dimensional extension fields of the rational numbers, algebraic number fields, and the rings of algebraic integers in them. The important theorems regarding the units of the ring of integers and the class group are proved and illustrated with many examples given in detail. The completion of an algebraic number field at a valuation is discussed in detail and then used to provide economical proofs of global results. The book contains many concrete examples illustrating the computation of class groups, class numbers, and Hilbert class fields. Exercises are provided to indicate applications of the general theory.
Book Synopsis Introduction To Non-abelian Class Field Theory, An: Automorphic Forms Of Weight 1 And 2-dimensional Galois Representations by : Toyokazu Hiramatsu
Download or read book Introduction To Non-abelian Class Field Theory, An: Automorphic Forms Of Weight 1 And 2-dimensional Galois Representations written by Toyokazu Hiramatsu and published by World Scientific. This book was released on 2016-09-13 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a brief exposition of automorphic forms of weight 1 and their applications to arithmetic, especially to Galois representations. One of the outstanding problems in arithmetic is a generalization of class field theory to non-abelian Galois extension of number fields. In this volume, we discuss some relations between this problem and cusp forms of weight 1.
Download or read book Number Fields written by Daniel A. Marcus and published by Springer. This book was released on 2018-07-05 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, pedestrian manner. It therefore avoids local methods and presents proofs in a way that highlights the important parts of the arguments. Readers are assumed to be able to fill in the details, which in many places are left as exercises.
Download or read book Number Fields written by Frans Keune and published by Radboud University Press. This book was released on 2023-03-27 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number Fields is a textbook for algebraic number theory. It grew out of lecture notes of master courses taught by the author at Radboud University, the Netherlands, over a period of more than four decades. It is self-contained in the sense that it uses only mathematics of a bachelor level, including some Galois theory. Part I of the book contains topics in basic algebraic number theory as they may be presented in a beginning master course on algebraic number theory. It includes the classification of abelian number fields by groups of Dirichlet characters. Class field theory is treated in Part II: the more advanced theory of abelian extensions of number fields in general. Full proofs of its main theorems are given using a ‘classical’ approach to class field theory, which is in a sense a natural continuation of the basic theory as presented in Part I. The classification is formulated in terms of generalized Dirichlet characters. This ‘ideal-theoretic’ version of class field theory dates from the first half of the twentieth century. In this book, it is described in modern mathematical language. Another approach, the ‘idèlic version’, uses topological algebra and group cohomology and originated halfway the last century. The last two chapters provide the connection to this more advanced idèlic version of class field theory. The book focuses on the abstract theory and contains many examples and exercises. For quadratic number fields algorithms are given for their class groups and, in the real case, for the fundamental unit. New concepts are introduced at the moment it makes a real difference to have them available.
Book Synopsis Class Groups of Number Fields and Related Topics by : Kalyan Chakraborty
Download or read book Class Groups of Number Fields and Related Topics written by Kalyan Chakraborty and published by Springer Nature. This book was released on 2020-01-17 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers original research papers and survey articles presented at the “International Conference on Class Groups of Number Fields and Related Topics,” held at Harish-Chandra Research Institute, Allahabad, India, on September 4–7, 2017. It discusses the fundamental research problems that arise in the study of class groups of number fields and introduces new techniques and tools to study these problems. Topics in this book include class groups and class numbers of number fields, units, the Kummer–Vandiver conjecture, class number one problem, Diophantine equations, Thue equations, continued fractions, Euclidean number fields, heights, rational torsion points on elliptic curves, cyclotomic numbers, Jacobi sums, and Dedekind zeta values. This book is a valuable resource for undergraduate and graduate students of mathematics as well as researchers interested in class groups of number fields and their connections to other branches of mathematics. New researchers to the field will also benefit immensely from the diverse problems discussed. All the contributing authors are leading academicians, scientists, researchers, and scholars.
Book Synopsis Algebraic Number Fields by : Albrecht Fröhlich
Download or read book Algebraic Number Fields written by Albrecht Fröhlich and published by . This book was released on 1977 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Classical Invitation to Algebraic Numbers and Class Fields by : Harvey Cohn
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"
Author :Lawrence C. Washington Publisher :Springer Science & Business Media ISBN 13 :9780387947624 Total Pages :508 pages Book Rating :4.9/5 (476 download)
Book Synopsis Introduction to Cyclotomic Fields by : Lawrence C. Washington
Download or read book Introduction to Cyclotomic Fields written by Lawrence C. Washington and published by Springer Science & Business Media. This book was released on 1997 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text on a central area of number theory covers p-adic L-functions, class numbers, cyclotomic units, Fermat’s Last Theorem, and Iwasawa’s theory of Z_p-extensions. This edition contains a new chapter on the work of Thaine, Kolyvagin, and Rubin, including a proof of the Main Conjecture, as well as a chapter on other recent developments, such as primality testing via Jacobi sums and Sinnott’s proof of the vanishing of Iwasawa’s f-invariant.
Book Synopsis Evaluating Zeta Functions of Abelian Number Fields at Negative Integers by : Dylan Attwell-Duval
Download or read book Evaluating Zeta Functions of Abelian Number Fields at Negative Integers written by Dylan Attwell-Duval and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Class Number Parity by : Pierre E. Conner
Download or read book Class Number Parity written by Pierre E. Conner and published by World Scientific. This book was released on 1988 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with classical questions of Algebraic Number Theory concerning the interplay between units, ideal class groups, and ramification for relative extensions of number fields. It includes a large collection of fundamental classical examples, dealing in particular with relative quadratic extensions as well as relative cyclic extensions of odd prime degree. The unified approach is exclusively algebraic in nature.
Book Synopsis Class Field Theory by : Nancy Childress
Download or read book Class Field Theory written by Nancy Childress and published by Springer Science & Business Media. This book was released on 2008-10-28 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Class field theory brings together the quadratic and higher reciprocity laws of Gauss, Legendre, and others, and vastly generalizes them. This book provides an accessible introduction to class field theory. It takes a traditional approach in that it attempts to present the material using the original techniques of proof, but in a fashion which is cleaner and more streamlined than most other books on this topic. It could be used for a graduate course on algebraic number theory, as well as for students who are interested in self-study. The book has been class-tested, and the author has included lots of challenging exercises throughout the text.
Book Synopsis On the Density of Abelian Number Fields by : Sirpa Mäki
Download or read book On the Density of Abelian Number Fields written by Sirpa Mäki and published by . This book was released on 1985 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Extremal Class Numbers of Non-abelian Number Fields by : Ryan Clark Daileda
Download or read book Extremal Class Numbers of Non-abelian Number Fields written by Ryan Clark Daileda and published by . This book was released on 2004 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:
