
rebetche pramey

rebetche pramey (purvi epsilon anuman kinwa ε-anuman mhatale jaate) haah sankhya siddhantacha eka bhag aahe. heey modular swarupanshi sambandhit gallois pratinidhitvanchya gunadharmanshi sambandhit aahe. too jeane-piyare serne prastavit keela hota aanee qeena rebetne siddha keela hota. haah purava haah farmatchya shevatchya pramey (eff. ell. tii.) chya puravyachya dishene eka mahattvapoorn paul hota. sair aanee rebetne darshavilyapramane, taniyama-shimura andaj (jyachi sthitee tyaveli nirakaran jhaleli navhati) aanee epsilon andaj ektritpane soochit karatat qee flt kharey aahe.
ganiteey drushtine, rebetche pramey darshavite qee jarr lambvartulakar vakraresheshi sambandhit gallois pratinidhitvamadhye kahee gunadharm asateel, tarr too vakr modular asoo shakat nahee (yaa arthane qee samaan pratinidhitvas janm denara modular form astitvat asoo shakat nahee).
vidhan.
- i varr vajan 2 naveen swaroop asoo dya.eae. jyaa staravar vibhajan hott nahee-purnapane irreducible 2-dimensional modd gallois pratinidhitvasaha, jarr yethe biin-shrenibaddha aanee maryadit sapat yethe. mug pataliche vajan 2 asey naveen swaroop astitvat aahe qee
visheshtah, jarr vahkasah sootra _ 2 varr lambvartulakar vakr asel, tarr modularity pramey hummy dete qee pataliche vajan 2 naveen swaroop astitvat aahe, jase qee 2-aayami modd galloische pratinidhitva 2-aayami modd galloischya pratinidhitvasathi samaroop aahe. rebetche pramey lagoo karnyasathi, tyachi irreducibility aanee parichhed tapasane purese aahe. tete vakratechya siddhantacha vapar karoon, kiman bhedbhavamadhye disana shaktiche vibhajan kelyas, ekhadi vyakti heey siddha karoo shakate qee teey biin-shrenikrut aanee maryadit sapat aahe. mug rebetche pramey soochit karate qee pataliche vajan 2 asey naveen swaroop astitvat aahe.
patali qamee karane.
rebatesche pramey asey sangate qee vahakachya lambvartulakar vakrareshepasun suruvat karane heey asha patalichya lambvartulakar vakrareshechya astitvachi hummy dett nahee. patalichya naveen swarupat tarksangat forier gunank nastil aanee mhanunach teey lambvartulakar vakr nahee tarr uchch-aayami abelian prakarashi sambandhit asoo shakatat. udaharanarth, samikaranadvare dilelya cremona detabasemadhil lambvartulakar vakr 4171a1
vahak aanee discriminants vahak 97 chya lambvartulakar vakrareshesathi modd 7 patali-qamee karat nahee. tyaeivaji, modd galloische pratinidhitva 97 chya staratil atarkik naveen swarupachya modd galloischya pratinidhitvasathi samaroop aahe.
tathapi, patali-qamee jhalelya naveen swarupachya patalichya tulanet purese mothe, eka tarksangat naveen swaroop (udaa.jee. lambvartulakar vakr) dusya tarksangat naveen swarupakade (udaa.jee. lambvartulakar vakr). visheshtah, tarksangat naveen swarupache modd gallois pratinidhitva patalichya atarkik naveen swarupasathi samaroop asoo shakat nahee.
tyachpramane, free-majur andaj assa andaj lavto qee puresha mothya (vahakapasoon swatantra) sathee, samaroop modd gallois pratinidhitvasaha lambvartulakar vakr pratyakshat samaroop asatat aanee mhanunach samaan vahak asatat. asha prakare tarksangat naveen swarupanmadhil kshullak patali-qamee hone mothya pramanat hoil assa andaj nahee.
itihas.
tyachya prabandhat, farmetchya samikaranachya upayanna ("aaa", "buub", "see") vegalya ganiteey vastushi jodanyachi kalpana udbhavalih eka lambvartulakar vakr. jarr "p" haah visham avibhajya asel aanee "a", "b" aanee "c" heey asey sakaratmak purnank asateel qee
mug sambandhit frey vakr haah samikaranadvare dilela bijganitiy vakr asato.
heey sootra _ 2 varr paribhashit kelelya vansh ekche eka ekras bijganitiy vakr aahe aanee tyache prakshepak purnatva sootra _ 2 varr lambvartulakar vakr aahe.
1982 madhye gerhard freeney tyach vakrareshechya asamanya gunadharmankade laksh vedhale, jyala aata free vakr mhanatat. yamule fermatt aanee taniyama darmyan eka pool upalabdh jhaala, heey dakhavun qee fltche prati-udaharan eka vakr tayar karel jeey modular nasel. taniyama-shimura-well andaj haah flt soochit karato asey freeney suchavale tevha yaa andajane lakshaniy swarasya aakarshit kele. matra, tyancha yuktivad purn jhaala nahee. 1985 madhye jeane-piyare serne prastavit kele qee eka free vakr modular asoo shakat nahee aanee anshatah purava pradan keela. yane asey disun aale qee taniyama-shimura andajachya ardh-sthir prakaranacha purava flt soochit karel. serne sampoorn purava deela nahee aanee haravalela biit epsilon anuman kinwa ε-anuman mhanoon olakhala jaau lagla. 1986 chya unhalyat, keneth alaan rebetne epsilon andaj siddha keela, jyamule heey siddha jhaale qee taniyama-shimura-well andaj haah flt soochit karato.
parinam.
samaja ghatankachya fermatt samikaranache uttar shunyetar purnankanmadhye hote. sambandhit frey vakr haah eka lambvartulakar vakr aahe jyacha kiman discriminant samaan aahe aanee jyacha vahak i chaa mooldrav aahe.eae. serve bhinn avibhajya bhaganche gunakar. samikaranacha prathamik vichar kelyas heey spasht hote qee eka summ aahe aanee mhanoon "aine" aahe. taniyama-shimura andajanusar, eka modular lambvartulakar vakr aahe. kaaran serve visham avibhajya ghatak kamitakami discriminantmadhye shakti darshavtat, rebetchya punaravrutti patalichya utaratya modulochya prameyanusar vahakatoon serve visham avibhajya ghatak kadhoon taktat. tathapi, star 2 chey konatehi naveen prakar shillak naheet kaaran modular vakratechi vanshasankhya shoonya aahe (aanee patali "aine" chey naveen prakar bhinn aahet.