The Riemann hypothesis in characteristic p in historical perspective / Peter Roquette.Material type: TextSeries: Lecture notes in mathematics (Springer-Verlag): 2222.; Lecture notes in mathematics (Springer-Verlag): Publisher: Cham : Springer, 2018Description: 1 online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783319990675; 3319990675; 9783319990682; 3319990683Subject(s): Riemann hypothesis | Characteristic functions | Algebraic fields | Characteristic functions | Algebraic fields | Riemann hypothesis | Mathematics -- Number Theory | Number theory | Mathematics -- History & Philosophy | History of mathematics | History of Mathematical Sciences | Number TheoryGenre/Form: Electronic books. Additional physical formats: Print version:: Riemann hypothesis in characteristic p in historical perspective.DDC classification: 512.7/3 LOC classification: QA3 | .L28 no. 2222Online resources: Click here to access online
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Includes bibliographical references and index.
Print version record.
Overture -- Setting the stage -- The beginning : Artin's thesis -- Building the foundations -- Enter Hasse -- Diophantine congruences -- Elliptic function fields -- More on elliptic fields -- Towards higher genus -- A virtual proof -- Intermission -- A. Weil -- Correction to: The Riemann Hypothesis in Characteristic p in Historical Perspective.
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.