02695nam a2200481 i 4500991003636349707536m o d cr |n|||||||||190409s2018 sz ob 001 0 eng d3319990675(electronic bk.)9783319990675(electronic bk.)3319990667978331999066810.1007/978-3-319-99067-5doib14363926-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng510.923AMS 11M26AMS 01A60AMS 11R58AMS 14H05LC QA3.L28Roquette, Peter58278The Riemann hypothesis in characteristic p in historical perspective[e-book] /Peter RoquetteCham :Springer,20181 online resource (ix, 235 p. 15 illus.)texttxtrdacontentcomputercrdamediaonline resourcecrrdacarrierLecture notes in mathematics,2193-1771 ;2222Includes bibliographical references and indexPreface -- 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. - IndexThis 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 fieldsNumber theoryRiemann hypothesisCharacteristic functionsAlgebraic fieldshttp://link.springer.com/10.1007/978-3-319-99067-5An electronic book accessible through the World Wide Web.b1436392603-03-2209-04-19991003636349707536Riemann hypothesis in characteristic p in historical perspective1749892UNISALENTOle01309-04-19m@ -engsz 40