Number Theory And Related Fields

Author : Jonathan M. Borwein,Igor Shparlinski,Wadim Zudilin
Publisher : Springer Science & Business Media
Page : 395 pages
File Size : 52,5 Mb
Release : 2013-05-16
Category : Mathematics
ISBN : 9781461466420

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Number Theory and Related Fields by Jonathan M. Borwein,Igor Shparlinski,Wadim Zudilin Pdf

“Number Theory and Related Fields” collects contributions based on the proceedings of the "International Number Theory Conference in Memory of Alf van der Poorten," hosted by CARMA and held March 12-16th 2012 at the University of Newcastle, Australia. The purpose of the conference was to promote number theory research in Australia while commemorating the legacy of Alf van der Poorten, who had written over 170 papers on the topic of number theory and collaborated with dozens of researchers. The research articles and surveys presented in this book were written by some of the most distinguished mathematicians in the field of number theory, and articles will include related topics that focus on the various research interests of Dr. van der Poorten.​

Author : Michael Rosen
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 40,9 Mb
Release : 2013-04-18
Category : Mathematics
ISBN : 9781475760460

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Number Theory in Function Fields by Michael Rosen Pdf

Early in the development of number theory, it was noticed that the ring of integers has many properties in common with the ring of polynomials over a finite field. The first part of this book illustrates this relationship by presenting analogues of various theorems. The later chapters probe the analogy between global function fields and algebraic number fields. Topics include the ABC-conjecture, Brumer-Stark conjecture, and Drinfeld modules.

Author : Daniel A. Marcus
Publisher : Springer
Page : 203 pages
File Size : 48,7 Mb
Release : 2018-07-05
Category : Mathematics
ISBN : 9783319902333

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Number Fields by Daniel A. Marcus Pdf

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.

Author : Jonathan M. Borwein,Igor Shparlinski,Wadim Zudilin
Publisher : Springer
Page : 0 pages
File Size : 46,8 Mb
Release : 2015-06-23
Category : Mathematics
ISBN : 1493902172

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Number Theory and Related Fields by Jonathan M. Borwein,Igor Shparlinski,Wadim Zudilin Pdf

“Number Theory and Related Fields” collects contributions based on the proceedings of the "International Number Theory Conference in Memory of Alf van der Poorten," hosted by CARMA and held March 12-16th 2012 at the University of Newcastle, Australia. The purpose of the conference was to promote number theory research in Australia while commemorating the legacy of Alf van der Poorten, who had written over 170 papers on the topic of number theory and collaborated with dozens of researchers. The research articles and surveys presented in this book were written by some of the most distinguished mathematicians in the field of number theory, and articles will include related topics that focus on the various research interests of Dr. van der Poorten.​

Author : David Chudnovsky,Gregory Chudnovsky,Melvyn B. Nathanson
Publisher : Springer Science & Business Media
Page : 272 pages
File Size : 55,5 Mb
Release : 2011-06-27
Category : Mathematics
ISBN : 9781441990600

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Number Theory by David Chudnovsky,Gregory Chudnovsky,Melvyn B. Nathanson Pdf

This volume of new research papers marks the 20th anniversary of the New York Number Theory Seminar (NYNTS). Since 1982, NYNTS has presented a range of research in number theory and related fields of mathematics, from physics to geometry to combinatorics and computer science. The speakers have included Field medalists as well as promising lesser known mathematicians whose theorems are significant. The papers presented here are all previously unpublished.

Author : Ed Norex
Publisher : Independently Published
Page : 0 pages
File Size : 55,8 Mb
Release : 2024-02-29
Category : Mathematics
ISBN : 9798883313461

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Introduction to Number Theory by Ed Norex Pdf

Unlock the mysteries of integers and their properties with "Introduction to Number Theory," your comprehensive guide to the fascinating world of number theory. From the basic principles of divisibility and primes to the intricate realms of elliptic curves and Fermat's Last Theorem, this book offers a meticulous exploration of the core concepts and advanced topics within number theory. Delve into the historical and practical applications, including its pivotal role in cryptography and digital security, and discover the beauty and utility of numbers through clear explanations, detailed examples, and engaging exercises. Designed for students, educators, and professionals, "Introduction to Number Theory" simplifies complex theories and techniques, making them accessible to readers with a basic understanding of algebra. Each chapter is carefully structured to build on prior knowledge, guiding you through the landscape of number theory with a direct and informative style. Whether you aim to solidify your understanding of number theory, seek to apply its principles in related fields, or simply are fascinated by the mathematical underpinnings of the digital world, this book is an invaluable resource. Embrace the opportunity to expand your mathematical horizons and uncover the secrets of number theory with "Introduction to Number Theory."

Author : Andre Weil
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 45,7 Mb
Release : 2013-12-14
Category : Mathematics
ISBN : 9783662059784

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Basic Number Theory. by Andre Weil Pdf

Itpzf}JlOV, li~oxov uoq>ZUJlCJ. 7:WV Al(JX., llpoj1. AE(Jj1. The first part of this volume is based on a course taught at Princeton University in 1961-62; at that time, an excellent set ofnotes was prepared by David Cantor, and it was originally my intention to make these notes available to the mathematical public with only quite minor changes. Then, among some old papers of mine, I accidentally came across a long-forgotten manuscript by ChevaIley, of pre-war vintage (forgotten, that is to say, both by me and by its author) which, to my taste at least, seemed to have aged very welt It contained abrief but essentially com plete account of the main features of c1assfield theory, both local and global; and it soon became obvious that the usefulness of the intended volume would be greatly enhanced if I inc1uded such a treatment of this topic. It had to be expanded, in accordance with my own plans, but its outline could be preserved without much change. In fact, I have adhered to it rather c10sely at some critical points.

Author : H. P. F. Swinnerton-Dyer
Publisher : Cambridge University Press
Page : 164 pages
File Size : 47,8 Mb
Release : 2001-02-22
Category : Mathematics
ISBN : 0521004233

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A Brief Guide to Algebraic Number Theory by H. P. F. Swinnerton-Dyer Pdf

Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.

Author : Jennifer S. Balakrishnan,Amanda Folsom,Matilde Lalín,Michelle Manes
Publisher : Springer
Page : 195 pages
File Size : 44,9 Mb
Release : 2019-08-01
Category : Mathematics
ISBN : 9783030194789

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Research Directions in Number Theory by Jennifer S. Balakrishnan,Amanda Folsom,Matilde Lalín,Michelle Manes Pdf

These proceedings collect several number theory articles, most of which were written in connection to the workshop WIN4: Women in Numbers, held in August 2017, at the Banff International Research Station (BIRS) in Banff, Alberta, Canada. It collects papers disseminating research outcomes from collaborations initiated during the workshop as well as other original research contributions involving participants of the WIN workshops. The workshop and this volume are part of the WIN network, aimed at highlighting the research of women and gender minorities in number theory as well as increasing their participation and boosting their potential collaborations in number theory and related fields.

Author : Jürgen Neukirch
Publisher : Springer Science & Business Media
Page : 583 pages
File Size : 48,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662039830

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Algebraic Number Theory by Jürgen Neukirch Pdf

This introduction to algebraic number theory discusses the classical concepts from the viewpoint of Arakelov theory. The treatment of class theory is particularly rich in illustrating complements, offering hints for further study, and providing concrete examples. It is the most up-to-date, systematic, and theoretically comprehensive textbook on algebraic number field theory available.

Author : W C Winnie Li
Publisher : World Scientific Publishing Company
Page : 244 pages
File Size : 45,9 Mb
Release : 1996-02-16
Category : Mathematics
ISBN : 9789813104853

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Number Theory with Applications by W C Winnie Li Pdf

Novel and important applications of number theory to graph theory and vice versa had been made in the past decade. The two main tools used are based on the estimates of character sums and the estimates of the eigenvalues of Hecke operators, both are rooted in the celebrated Weil conjectures settled by Deligne in 1973. The purpose of this book is to give, from scratch, a coherent and comprehensive introduction to the topics in number theory related to the central tools, with the ultimate goal of presenting their applications. This book includes many important subjects in number theory, such as Weil conjectures, Riemann-Roch theorem, L-functions, character sum estimates, modular forms, and representation theory. Request Inspection Copy

Author : Kazuya Kato,Nobushige Kurokawa,Takeshi Saitō,Masato Kurihara
Publisher : American Mathematical Soc.
Page : 258 pages
File Size : 46,8 Mb
Release : 2000
Category : Class field theory
ISBN : 9780821813553

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Number Theory by Kazuya Kato,Nobushige Kurokawa,Takeshi Saitō,Masato Kurihara Pdf

Author : Robert L. Long
Publisher : Unknown
Page : 216 pages
File Size : 45,5 Mb
Release : 1977
Category : Mathematics
ISBN : UOM:39015015612396

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Algebraic Number Theory by Robert L. Long Pdf

Author : Marty Lewinter,Jeanine Meyer
Publisher : John Wiley & Sons
Page : 240 pages
File Size : 47,9 Mb
Release : 2015-06-02
Category : Mathematics
ISBN : 9781119062769

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Elementary Number Theory with Programming by Marty Lewinter,Jeanine Meyer Pdf

A highly successful presentation of the fundamental concepts of number theory and computer programming Bridging an existing gap between mathematics and programming, Elementary Number Theory with Programming provides a unique introduction to elementary number theory with fundamental coverage of computer programming. Written by highly-qualified experts in the fields of computer science and mathematics, the book features accessible coverage for readers with various levels of experience and explores number theory in the context of programming without relying on advanced prerequisite knowledge and concepts in either area. Elementary Number Theory with Programming features comprehensive coverage of the methodology and applications of the most well-known theorems, problems, and concepts in number theory. Using standard mathematical applications within the programming field, the book presents modular arithmetic and prime decomposition, which are the basis of the public-private key system of cryptography. In addition, the book includes: Numerous examples, exercises, and research challenges in each chapter to encourage readers to work through the discussed concepts and ideas Select solutions to the chapter exercises in an appendix Plentiful sample computer programs to aid comprehension of the presented material for readers who have either never done any programming or need to improve their existing skill set A related website with links to select exercises An Instructor’s Solutions Manual available on a companion website Elementary Number Theory with Programming is a useful textbook for undergraduate and graduate-level students majoring in mathematics or computer science, as well as an excellent supplement for teachers and students who would like to better understand and appreciate number theory and computer programming. The book is also an ideal reference for computer scientists, programmers, and researchers interested in the mathematical applications of programming.

Author : Harvey Cohn
Publisher : Courier Corporation
Page : 292 pages
File Size : 45,9 Mb
Release : 1980-08-01
Category : Mathematics
ISBN : 048664023X

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Advanced Number Theory by Harvey Cohn Pdf

"A very stimulating book ... in a class by itself." — American Mathematical Monthly Advanced students, mathematicians and number theorists will welcome this stimulating treatment of advanced number theory, which approaches the complex topic of algebraic number theory from a historical standpoint, taking pains to show the reader how concepts, definitions and theories have evolved during the last two centuries. Moreover, the book abounds with numerical examples and more concrete, specific theorems than are found in most contemporary treatments of the subject. The book is divided into three parts. Part I is concerned with background material — a synopsis of elementary number theory (including quadratic congruences and the Jacobi symbol), characters of residue class groups via the structure theorem for finite abelian groups, first notions of integral domains, modules and lattices, and such basis theorems as Kronecker's Basis Theorem for Abelian Groups. Part II discusses ideal theory in quadratic fields, with chapters on unique factorization and units, unique factorization into ideals, norms and ideal classes (in particular, Minkowski's theorem), and class structure in quadratic fields. Applications of this material are made in Part III to class number formulas and primes in arithmetic progression, quadratic reciprocity in the rational domain and the relationship between quadratic forms and ideals, including the theory of composition, orders and genera. In a final concluding survey of more recent developments, Dr. Cohn takes up Cyclotomic Fields and Gaussian Sums, Class Fields and Global and Local Viewpoints. In addition to numerous helpful diagrams and tables throughout the text, appendices, and an annotated bibliography, Advanced Number Theory also includes over 200 problems specially designed to stimulate the spirit of experimentation which has traditionally ruled number theory.