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Author : Michael Henry Merritt
Publisher :
ISBN 13 :
Total Pages : 72 pages
Book Rating : 4.:/5 (592 download)
Download or read book The Imaginary Quadratic Fields of Class Number Two written by Michael Henry Merritt and published by . This book was released on 1962 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Larry Joel Goldstein
Publisher :
ISBN 13 :
Total Pages : 52 pages
Book Rating : 4.:/5 (555 download)
Download or read book Imaginary Quadratic Fields of Class Number 2 written by Larry Joel Goldstein and published by . This book was released on 1970 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Paulo Ribenboim
Publisher : Springer Science & Business Media
ISBN 13 : 0387227547
Total Pages : 384 pages
Book Rating : 4.3/5 (872 download)
Download or read book My Numbers, My Friends written by Paulo Ribenboim and published by Springer Science & Business Media. This book was released on 2006-05-10 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This selection of expository essays by Paulo Ribenboim should be of interest to mathematicians from all walks. Ribenboim, a highly praised author of several popular titles, writes each essay in a light and humorous language without secrets, making them thoroughly accessible to everyone with an interest in numbers. This new collection includes essays on Fibonacci numbers, prime numbers, Bernoulli numbers, and historical presentations of the main problems pertaining to elementary number theory, such as Kummers work on Fermat's last theorem.
Author : David A. Cox
Publisher : John Wiley & Sons
ISBN 13 : 1118031008
Total Pages : 372 pages
Book Rating : 4.1/5 (18 download)
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.
Author : Mark James Watkins
Publisher :
ISBN 13 :
Total Pages : 282 pages
Book Rating : 4.:/5 (457 download)
Download or read book Class Numbers of Imaginary Quadratic Fields written by Mark James Watkins and published by . This book was released on 2000 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Institute for Defense Analyses. Supercomputing Research Center
Publisher :
ISBN 13 :
Total Pages : 34 pages
Book Rating : 4.:/5 (123 download)
Download or read book The Imaginary Quadratic Fields for Class Number 4 written by Institute for Defense Analyses. Supercomputing Research Center and published by . This book was released on 1988 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Praveen Agarwal
Publisher : Springer
ISBN 13 : 9811330131
Total Pages : 349 pages
Book Rating : 4.8/5 (113 download)
Download or read book Advances in Mathematical Inequalities and Applications written by Praveen Agarwal and published by Springer. This book was released on 2018-12-31 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of original research and survey articles on mathematical inequalities and their numerous applications in diverse areas of mathematics and engineering. It includes chapters on convexity and related concepts; inequalities for mean values, sums, functions, operators, functionals, integrals and their applications in various branches of mathematics and related sciences; fractional integral inequalities; and weighted type integral inequalities. It also presents their wide applications in biomathematics, boundary value problems, mechanics, queuing models, scattering, and geomechanics in a concise, but easily understandable way that makes the further ramifications and future directions clear. The broad scope and high quality of the contributions make this book highly attractive for graduates, postgraduates and researchers. All the contributing authors are leading international academics, scientists, researchers and scholars.
Author : Harvey Cohn
Publisher : Courier Corporation
ISBN 13 : 0486149242
Total Pages : 289 pages
Book Rating : 4.4/5 (861 download)
Download or read book Advanced Number Theory written by Harvey Cohn and published by Courier Corporation. This book was released on 2012-05-04 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eminent mathematician/teacher approaches algebraic number theory from historical standpoint. Demonstrates how concepts, definitions, and theories have evolved during last two centuries. Features over 200 problems and specific theorems. Includes numerous graphs and tables.
Author : Franz Lemmermeyer
Publisher : Springer Nature
ISBN 13 : 3030786528
Total Pages : 348 pages
Book Rating : 4.0/5 (37 download)
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.
Author : Kalyan Chakraborty
Publisher : Springer Nature
ISBN 13 : 981151514X
Total Pages : 182 pages
Book Rating : 4.8/5 (115 download)
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.
Author : Omer Kucuksakalli
Publisher :
ISBN 13 :
Total Pages : 75 pages
Book Rating : 4.:/5 (55 download)
Download or read book Class Numbers of Ray Class Fields of Imaginary Quadratic Fields written by Omer Kucuksakalli and published by . This book was released on 2009 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : R. A. Mollin
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (897 download)
Download or read book On Real Quadratic Fields of Class Number 2 written by R. A. Mollin and published by . This book was released on 1989 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hans Heilbronn
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (724 download)
Download or read book On the Class-number in Imaginary Quadratic Fields written by Hans Heilbronn and published by . This book was released on 1934 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Henri Darmon
Publisher : Cambridge University Press
ISBN 13 : 9780521836593
Total Pages : 386 pages
Book Rating : 4.8/5 (365 download)
Download or read book Heegner Points and Rankin L-Series written by Henri Darmon and published by Cambridge University Press. This book was released on 2004-06-21 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thirteen articles by leading contributors on the history of the Gross-Zagier formula and its developments.
Author : Alan Baker
Publisher : Cambridge University Press
ISBN 13 : 1009229966
Total Pages : pages
Book Rating : 4.0/5 (92 download)
Download or read book Transcendental Number Theory written by Alan Baker and published by Cambridge University Press. This book was released on 2022-06-09 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1975, this classic book gives a systematic account of transcendental number theory, that is, the theory of those numbers that cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory, which continues to see rapid progress today. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalization of the Thue–Siegel–Roth theorem, of Shidlovsky's work on Siegel's E-functions and of Sprindžuk's solution to the Mahler conjecture. This edition includes an introduction written by David Masser describing Baker's achievement, surveying the content of each chapter and explaining the main argument of Baker's method in broad strokes. A new afterword lists recent developments related to Baker's work.
Author : H. Koch
Publisher : Springer Science & Business Media
ISBN 13 : 9783540630036
Total Pages : 280 pages
Book Rating : 4.6/5 (3 download)
Download or read book Algebraic Number Theory written by H. Koch and published by Springer Science & Business Media. This book was released on 1997-09-12 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews of the first printing, published as Volume 62 of the Encyclopaedia of Mathematical Sciences: "... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." Monatshefte fuer Mathematik, 1994 "... Koch's book is written mostly for non-specialists. It is an up-to-date account of the subject dealing with mostly general questions. Special results appear only as illustrating examples for the general features of the theory. It is supposed that the reader has good general background in the fields of modern (abstract) algebra and elementary number theory. We recommend this volume mainly to graduate studens and research mathematicians." Acta Scientiarum Mathematicarum, 1993
Author : Wladyslaw Narkiewicz
Publisher : Springer Science & Business Media
ISBN 13 : 3662070014
Total Pages : 712 pages
Book Rating : 4.6/5 (62 download)
Download or read book Elementary and Analytic Theory of Algebraic Numbers written by Wladyslaw Narkiewicz and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book details the classical part of the theory of algebraic number theory, excluding class-field theory and its consequences. Coverage includes: ideal theory in rings of algebraic integers, p-adic fields and their finite extensions, ideles and adeles, zeta-functions, distribution of prime ideals, Abelian fields, the class-number of quadratic fields, and factorization problems. The book also features exercises and a list of open problems.
