Overview
- 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
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2222)
Part of the book sub series: History of Mathematics Subseries (HISTORYMS)
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Table of contents (14 chapters)
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Front Matter
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Back Matter
Keywords
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.
Reviews
“This is a rich and illuminating study of the mathematical developments over the period 1921-1942 that led to the proof by André Weil of the Riemann Hypothesis for algebraic function fields over a finite field of characteristic p (RHp). … Mathematicians with some knowledge of modern algebra and field theory will follow the main thread of the story, since the author avoids a heavily technical discussion.” (E. J. Barbeau, Mathematical Reviews, July, 2019)
“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)
Authors and Affiliations
About the author
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.
Bibliographic Information
Book Title: The Riemann Hypothesis in Characteristic p in Historical Perspective
Authors: Peter Roquette
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-99067-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Softcover ISBN: 978-3-319-99066-8Published: 15 October 2018
eBook ISBN: 978-3-319-99067-5Published: 28 September 2018
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: IX, 235
Number of Illustrations: 15 b/w illustrations