The Riemann Hypothesis in Characteristic p in Historical Perspective

  • Peter Roquette

Part of the Lecture Notes in Mathematics book series (LNM, volume 2222)

Also part of the History of Mathematics Subseries book sub series (HISTORYMS, volume 2222)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Peter Roquette
    Pages 1-8
  3. Peter Roquette
    Pages 9-12
  4. Peter Roquette
    Pages 13-37
  5. Peter Roquette
    Pages 39-54
  6. Peter Roquette
    Pages 55-57
  7. Peter Roquette
    Pages 59-79
  8. Peter Roquette
    Pages 81-106
  9. Peter Roquette
    Pages 107-129
  10. Peter Roquette
    Pages 131-156
  11. Peter Roquette
    Pages 157-179
  12. Peter Roquette
    Pages 181-202
  13. Peter Roquette
    Pages 203-213
  14. Peter Roquette
    Pages 215-219
  15. Back Matter
    Pages 221-235

About this book


This book tells the story of the Riemann hypothesis for function fields (or curves) starting with Artin's 1921 thesis, covering Hasse's work in the 1930s on elliptic fields and more, and concluding with Weil's final proof in 1948. The main sources are letters which were exchanged among the protagonists during that time, found in various archives, mostly the University Library in Göttingen. The aim is to show how the ideas formed, and how the proper notions and proofs were found, providing a particularly well-documented illustration of how mathematics develops in general. The book is written for mathematicians, but it does not require any special knowledge of particular mathematical fields.


Riemann hypothesis in characteristic p Emil Artin Helmut Hasse André Weil History of Number Theory in the 20th century

Authors and affiliations

  • Peter Roquette
    • 1
  1. 1.Mathematical InstituteHeidelberg UniversityHeidelbergGermany

Bibliographic information

  • DOI
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-99066-8
  • Online ISBN 978-3-319-99067-5
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking