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Reassessing Riemann's Paper

On the Number of Primes Less Than a Given Magnitude

  • Walter Dittrich

Part of the SpringerBriefs in History of Science and Technology book series (BRIEFSHIST)

Table of contents

About this book

Introduction

In this book, the author pays tribute to Bernhard Riemann (1826–1866), mathematician with revolutionary ideas, whose work on the theory of integration, the Fourier transform, the hypergeometric differential equation, etc. contributed immensely to mathematical physics. This book concentrates in particular on Riemann’s only work on prime numbers, including such then new ideas as analytical continuation in the complex plane and the product formula for entire functions. A detailed analysis of the zeros of the Riemann zeta function is presented. The impact of Riemann’s ideas on regularizing infinite values in field theory is also emphasized.

Keywords

Riemann's Paper on Prime Numbers Zeta-function regularization Functional equation Fourier transform Riemann's function Mangoldt's formula Zeros of zeta function and critical strip History of prime number theory

Authors and affiliations

  • Walter Dittrich
    • 1
  1. 1.Institut für Theoretische PhysikUniversität TübingenTübingenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-91482-4
  • Copyright Information The Author(s) 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-91481-7
  • Online ISBN 978-3-319-91482-4
  • Series Print ISSN 2211-4564
  • Series Online ISSN 2211-4572
  • Buy this book on publisher's site