This book surveys 20th century progress in classical number theory, from the proof of the Prime Number Theorem in 1896 through the proof of Fermat's Last Theorem, focusing on the part of number theory that addresses properties of integers and rational numbers.

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.

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. Includes supplementary material: sn.pub/extras

Autorentext

Wladyslaw Narkiewicz is a Polish mathematician who is particularly active in the fields of (analytic) number theory, algebra and the history of mathematics. He received his PhD in 1961 and his habilitation in 1967 at the University of Wroclaw, where he also taught from 1974 to 2006 as a full professor. He is the author of several Springer books, among which the "Rational Number Theory in the 20th Century" and "The Development of Prime Number Theory". Narkiewicz held during his career various administrative functions at the University of Wroclaw, including Deputy Head of the Mathematical Institute, Dean of the Faculty of Mathematics and Physics and Vice Rector for Scientific Affairs. In 1968 he was awarded the Stefan Banach Prize.

Inhalt
The Heritage.- The First Years.- The Twenties.- The Thirties.- The Forties and Fifties.- The Last Period.- Fermat's Last Theorem