LEADER 02695nam a2200481 i 4500 001 991003636349707536 006 m o d 007 cr |n||||||||| 008 190409s2018 sz ob 001 0 eng d 020 $a3319990675$q(electronic bk.) 020 $a9783319990675$q(electronic bk.) 020 $z3319990667 020 $z9783319990668 024 7 $a10.1007/978-3-319-99067-5$2doi 035 $ab14363926-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 082 04$a510.9$223 084 $aAMS 11M26 084 $aAMS 01A60 084 $aAMS 11R58 084 $aAMS 14H05 084 $aLC QA3.L28 100 1 $aRoquette, Peter$058278 245 14$aThe Riemann hypothesis in characteristic p in historical perspective$h[e-book] /$cPeter Roquette 264 1$aCham :$bSpringer,$c2018 300 $a1 online resource (ix, 235 p. 15 illus.) 336 $atext$btxt$2rdacontent 337 $acomputer$bc$2rdamedia 338 $aonline resource$bcr$2rdacarrier 490 1 $aLecture notes in mathematics,$x2193-1771 ;$v2222 504 $aIncludes bibliographical references and index 505 0 $aPreface -- 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 520 $aThis book tells the story of the Riemann hypothesis for function fields (or curves) starting with Artin's 1921 thesis, covering Hasse's work in the 1930s on elliptic fields and more, and concluding with Weil's final proof in 1948. The main sources are letters which were exchanged among the protagonists during that time, found in various archives, mostly the University Library in Göttingen. The aim is to show how the ideas formed, and how the proper notions and proofs were found, providing a particularly well-documented illustration of how mathematics develops in general. The book is written for mathematicians, but it does not require any special knowledge of particular mathematical fields 650 0$aNumber theory 650 0$aRiemann hypothesis 650 0$aCharacteristic functions 650 0$aAlgebraic fields 856 40$uhttp://link.springer.com/10.1007/978-3-319-99067-5$zAn electronic book accessible through the World Wide Web 907 $a.b14363926$b03-03-22$c09-04-19 912 $a991003636349707536 996 $aRiemann hypothesis in characteristic p in historical perspective$91749892 997 $aUNISALENTO 998 $ale013$b09-04-19$cm$d@ $e-$feng$gsz $h4$i0