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Springer Monographs in Mathematics

The Development of Prime Number Theory

From Euclid to Hardy and Littlewood

Authors: Narkiewicz, Wladyslaw

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eBook 118,99 €
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  • ISBN 978-3-662-13157-2
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Hardcover 155,95 €
price for Spain (gross)
  • ISBN 978-3-540-66289-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Softcover 155,95 €
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  • ISBN 978-3-642-08557-4
  • 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
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.

Table of contents (6 chapters)

  • Early Times

    Narkiewicz, Władysław

    Pages 1-47

    Preview Buy Chapter 30,19 €
  • Dirichlet’s Theorem on Primes in Arithmetic Progressions

    Narkiewicz, Władysław

    Pages 49-96

    Preview Buy Chapter 30,19 €
  • Čebyšev’s Theorem

    Narkiewicz, Władysław

    Pages 97-132

    Preview Buy Chapter 30,19 €
  • Riemann’s Zeta-function and Dirichlet Series

    Narkiewicz, Władysław

    Pages 133-182

    Preview Buy Chapter 30,19 €
  • The Prime Number Theorem

    Narkiewicz, Władysław

    Pages 183-255

    Preview Buy Chapter 30,19 €

Buy this book

eBook 118,99 €
price for Spain (gross)
  • ISBN 978-3-662-13157-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 155,95 €
price for Spain (gross)
  • ISBN 978-3-540-66289-1
  • 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 155,95 €
price for Spain (gross)
  • ISBN 978-3-642-08557-4
  • 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
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Bibliographic Information

Bibliographic Information
Book Title
The Development of Prime Number Theory
Book Subtitle
From Euclid to Hardy and Littlewood
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2000
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-13157-2
DOI
10.1007/978-3-662-13157-2
Hardcover ISBN
978-3-540-66289-1
Softcover ISBN
978-3-642-08557-4
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XII, 449
Topics