History of Mathematics Subseries

The Riemann Hypothesis in Characteristic p in Historical Perspective

Authors: Roquette, Peter

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  • Describes the history of the Riemann hypothesis for function fields based on letters exchanged between the main protagonists at the time
  • Provides a well-documented account of how mathematics develops in general
  • Written for mathematicians, but does not require specialist knowledge
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eBook $39.99
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  • ISBN 978-3-319-99067-5
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  • Immediate eBook download after purchase
Softcover $54.99
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  • ISBN 978-3-319-99066-8
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  • Usually dispatched within 3 to 5 business days.
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.

About the authors

Roquette studierte in Erlangen, Berlin und Hamburg und wurde 1951 an der Universität Hamburg bei Helmut Hasse promoviert, Ab 1967 ist er Professor an der Ruprecht-Karls-Universität Heidelberg, an der er 1996 emeritiert wurde. Roquette arbeitet über Zahl- und Funktionenkörper und speziell lokale p-adische Körper. Er wandte auch Methoden der Modelltheorie (Nonstandard Arithmetic) in der Zahlentheorie an, teilweise noch mit Abraham Robinson.. Er hat auch eine Reihe von Arbeiten zur Geschichte der Mathematik, insbesondere der Schulen von Helmut Hasse und Emmy Noether veröffentlicht. Roquette war 1975 Mitherausgeber der gesammelten Abhandlungen von Helmut Hasse und gab eine Zahlentheorie-Vorlesung von Erich Hecke aus dem Jahr 1920 neu heraus. Roquette ist seit 1978 Mitglied der Heidelberger Akademie der Wissenschaften[3] und seit 1985 der Deutschen Akademie der Naturforscher Leopoldina[4] sowie Ehrendoktor der Universität Duisburg-Essen und Ehrenmitglied der Mathematischen Gesellschaft Hamburg.

Reviews

“The book is very pleasant to read and should be consulted by any one interested in history, in function fields or in general in the RH in any characteristic. The book can be used by specialists and by non-specialists as a brief but very interesting introduction to function fields including its relation with algebraic geometry. … The summaries give a good abstract of the book.” (Gabriel D. Villa Salvador, zbMath 1414.11003, 2019)

Table of contents (14 chapters)

Table of contents (14 chapters)

Buy this book

eBook $39.99
price for Mexico (gross)
  • ISBN 978-3-319-99067-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for Mexico
  • ISBN 978-3-319-99066-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Riemann Hypothesis in Characteristic p in Historical Perspective
Authors
Series Title
History of Mathematics Subseries
Series Volume
2222
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-319-99067-5
DOI
10.1007/978-3-319-99067-5
Softcover ISBN
978-3-319-99066-8
Series ISSN
2193-1771
Edition Number
1
Number of Pages
IX, 235
Number of Illustrations
15 b/w illustrations
Topics