Springer Monographs in Mathematics

Rational Number Theory in the 20th Century

From PNT to FLT

Authors: Narkiewicz, Wladyslaw

  • Accessible to non-experts as it presents the main results in the field without detailing the technicalities.
  • Offers an overview of 20th century developments in classical number theory for the first time.
  • Includes an extensive bibliography with over 4,000 references.
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eBook 83,29 €
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  • ISBN 978-0-85729-532-3
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Hardcover 103,99 €
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  • ISBN 978-0-85729-531-6
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Softcover 103,99 €
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  • ISBN 978-1-4471-2715-4
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About this book

The last one hundred years have seen many important achievements in the classical part of number theory. After the proof of the Prime Number Theorem in 1896, a quick development of analytical tools led to the invention of various new methods, like Brun's sieve method and the circle method of Hardy, Littlewood and Ramanujan; developments in topics such as prime and additive number theory, and the solution of Fermat’s problem. Rational Number Theory in the 20th Century: From PNT to FLT offers a short survey of 20th century developments in classical number theory, documenting between the proof of the Prime Number Theorem and the proof of Fermat's Last Theorem. The focus lays upon the part of number theory that deals with properties of integers and rational numbers. Chapters are divided into five time periods, which are then further divided into subject areas. With the introduction of each new topic, developments are followed through to the present day. This book will appeal to graduate researchers and student in number theory, however the presentation of main results without technicalities will make this accessible to anyone with an interest in the area.

Reviews

“This impressive book gives a comprehensive account of the developments of large parts of number theory in the twentieth century. … The result of the author’s endeavours is a magnificent work of reference which contains 6849 references on 235 pages and informs its reader on all important developments within the book’s scope. For anyone who is serious about number theory it will be indispensable for many years to come.” (Ch. Baxa, Monatshefte für Mathematik, Vol. 178 (1), 2015)

“This is an impressive effort to provide an annotated history of a large chunk of number-theoretic research during the 20th century. This volume can serve as a useful resource to current researchers in rational number theory and as an inspiration to future generations of mathematicians. As such, it would be a worthwhile investment for any self-respecting research mathematics library.” (Angel V. Kumchev, Mathematical Reviews, May, 2014)

“The book is an outstanding piece of work; it contains 6849 references, as well as an author index and a subject index, and it will be an invaluable source both for mathematicians working in number theory as well as for those interested in the history of mathematics of the 20th century.” (Franz Lemmermeyer, Zentralblatt MATH, Vol. 1230, 2012)


Table of contents (7 chapters)

Buy this book

eBook 83,29 €
price for Spain (gross)
  • ISBN 978-0-85729-532-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 103,99 €
price for Spain (gross)
  • ISBN 978-0-85729-531-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 103,99 €
price for Spain (gross)
  • ISBN 978-1-4471-2715-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Rational Number Theory in the 20th Century
Book Subtitle
From PNT to FLT
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2012
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London Limited
eBook ISBN
978-0-85729-532-3
DOI
10.1007/978-0-85729-532-3
Hardcover ISBN
978-0-85729-531-6
Softcover ISBN
978-1-4471-2715-4
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XIV, 654
Topics