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Lecture Notes in Mathematics Ser.: Riemann Hypothesis in Characteristic P in Historical Perspective by Peter Roquette (2018, Trade Paperback)
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About this product
Product Identifiers
PublisherSpringer International Publishing A&G
ISBN-103319990667
ISBN-139783319990668
eBay Product ID (ePID)19038687610
Product Key Features
Number of PagesIX, 235 Pages
Publication NameRiemann Hypothesis in Characteristic P in Historical Perspective
LanguageEnglish
Publication Year2018
SubjectHistory & Philosophy, Number Theory
TypeTextbook
AuthorPeter Roquette
Subject AreaMathematics
SeriesLecture Notes in Mathematics Ser.
FormatTrade Paperback
Dimensions
Item Weight16 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
TitleLeadingThe
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), "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), "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 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)
Series Volume Number2222
Number of Volumes1 vol.
IllustratedYes
Table Of Content- 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. - Appendix. - References. - Index.
SynopsisThis 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 G ttingen. 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., - 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. - Appendix. - References. - Index., 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.
LC Classification NumberQA21-27
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