The Riemann Hypothesis in Characteristic p in Historical Perspective (häftad)
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Format
Häftad (Paperback / softback)
Språk
Engelska
Antal sidor
235
Utgivningsdatum
2018-10-15
Upplaga
1st ed. 2018
Förlag
Springer International Publishing AG
Illustratör/Fotograf
Bibliographie 6 schwarz-weiße Abbildungen
Illustrationer
15 Illustrations, black and white; IX, 235 p. 15 illus.
Dimensioner
234 x 156 x 13 mm
Vikt
354 g
Antal komponenter
1
Komponenter
1 Paperback / softback
ISBN
9783319990668

The Riemann Hypothesis in Characteristic p in Historical Perspective

av Peter Roquette
Häftad,  Engelska, 2018-10-15
347
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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 Gttingen. 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.
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The book will be read by mathematicians and historians of mathematics beyond those whose primary interests are in the fields discussed here, and one could only wish that more people knew enough mathematics to follow the history it considers. (Arkady Plotnitsky, Isis, Vol. 111 (2), 2020) This is a rich and illuminating study of the mathematical developments over the period 1921-1942 that led to the proof by Andr 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)

Övrig information

Roquette studierte in Erlangen, Berlin und Hamburg und wurde 1951 an der Universitt Hamburg bei Helmut Hasse promoviert, Ab 1967 ist er Professor an der Ruprecht-Karls-Universitt Heidelberg, an der er 1996 emeritiert wurde. Roquette arbeitet ber Zahl- und Funktionenkrper und speziell lokale p-adische Krper. 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 verffentlicht. 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 Universitt Duisburg-Essen und Ehrenmitglied der Mathematischen Gesellschaft Hamburg.

Innehållsförteckning

- Overture.- Setting the stage.- The Beginning: Artins Thesis.- Building the Foundations.- Enter Hasse. - Diophantine Congruences. - Elliptic Function Fields. - More on Elliptic Fields. - Towards Higher Genus. - A Virtual Proof. - Intermission. - A.Weil. - Appendix. - References. - Index.

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