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The Development of Prime Number Theory

From Euclid to Hardy and Littlewood

  • Book
  • © 2000

Overview

Authors:
  1. Władysław Narkiewicz

    1. Institute of Mathematics, Wrocław University, Wrocław, Poland

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  • This book presents the history of prime numbers before 1926
  • Its aim is to present the main results and proofs and to outline the development of methods with which such problems were attacked in the course of time
  • It can be read by any person with the knowledge of the fundamental notions of number theory and complex analysis

Part of the book series: Springer Monographs in Mathematics (SMM)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-XII
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  2. Early Times

    • Władysław Narkiewicz
    Pages 1-47

  3. Dirichlet’s Theorem on Primes in Arithmetic Progressions

    • Władysław Narkiewicz
    Pages 49-96

  4. Čebyšev’s Theorem

    • Władysław Narkiewicz
    Pages 97-132

  5. Riemann’s Zeta-function and Dirichlet Series

    • Władysław Narkiewicz
    Pages 133-182

  6. The Prime Number Theorem

    • Władysław Narkiewicz
    Pages 183-255

  7. The Turn of the Century

    • Władysław Narkiewicz
    Pages 257-353

  8. Back Matter

    Pages 355-449
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Keywords

About this book

1. People were already interested in prime numbers in ancient times, and the first result concerning the distribution of primes appears in Euclid's Elemen­ ta, where we find a proof of their infinitude, now regarded as canonical. One feels that Euclid's argument has its place in The Book, often quoted by the late Paul ErdOs, where the ultimate forms of mathematical arguments are preserved. Proofs of most other results on prime number distribution seem to be still far away from their optimal form and the aim of this book is to present the development of methods with which such problems were attacked in the course of time. This is not a historical book since we refrain from giving biographical details of the people who have played a role in this development and we do not discuss the questions concerning why each particular person became in­ terested in primes, because, usually, exact answers to them are impossible to obtain. Our idea is to present the development of the theory of the distribu­ tion of prime numbers in the period starting in antiquity and concluding at the end of the first decade of the 20th century. We shall also present some later developments, mostly in short comments, although the reader will find certain exceptions to that rule. The period of the last 80 years was full of new ideas (we mention only the applications of trigonometrical sums or the advent of various sieve methods) and certainly demands a separate book.

Reviews

“This is a most welcome addition to the literature on prime numbers, zeta and L-functions and arithmetical functions. … The style is clear, with just the right amount of details. Each chapter closes with carefully chosen Exercises. Novices and experts alike will find that this a book of highest quality, which sets a standard for future works dealing with the history of Mathematics.” (A.Ivić, zbMATH 0942.11002, 2021)

Authors and Affiliations

  • Institute of Mathematics, Wrocław University, Wrocław, Poland

    Władysław Narkiewicz

Bibliographic Information

  • Book Title: The Development of Prime Number Theory

  • Book Subtitle: From Euclid to Hardy and Littlewood

  • Authors: Władysław Narkiewicz

  • Series Title: Springer Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-662-13157-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2000

  • Hardcover ISBN: 978-3-540-66289-1Published: 14 April 2000

  • Softcover ISBN: 978-3-642-08557-4Published: 07 December 2010

  • eBook ISBN: 978-3-662-13157-2Published: 14 March 2013

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 1

  • Number of Pages: XII, 449

  • Topics: Number Theory, History, general, Analysis, History of Mathematical Sciences

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