rebate kii pramey

rebate kii pramey (jise pahale apsilon anuman yaa ε-anuman kahaa jaataa thaa) sankhya siddhant kaa hissa haye. yeh modular roopon seey judey gallois pratinidhitva key gunon seey sambandhit haye. ise jeane-piyare sair dwara prastaavit kiya gayaa thaa aur caine rebate dwara siddh kiya gayaa thaa. yeh pramaan firmate kii antim pramey (aff. ell. tii.) key pramaan kii disha mein ack mahatvapurna kadam thaa. jaisa kii sair aur rebate dwara dikhaaya gayaa haye, taniyama-shimura anuman (jisaki sthiti usa samay ansuljhi thee) aur apsilon anuman ack saath ingit karate hain kii flt sach haye.
ganitiya sandarbh mein, rebate kii pramey seey pataa chalata haye kii yadi ack dirghvrittakar vakr seey judey gallois pratinidhitva mein kuchh guna hain, tou vaha vakr modular naheen hoe sakata haye (iss arth mein kii ack modular roop maujood naheen hoe sakata haye joe samaan pratinidhitva koo janm detaa haye).
bayaan.
chalo ack vajan 2 nayaa roop-i parr hoe.ee. star kaa jahan vibhajit naheen hotaa haye-bilkul aparivartaniya 2-ayami modd gallois pratinidhitva key saath yadi parr aur seemit sapaat parr. taba star kaa ack nayaa roop haye joe vajan 2 haye
vishesh roop seey, yadi conductor key saath sootra _ 2 parr ack andakar vakr haye, tou modularta pramey guaranti detaa haye kii star kaa ack vajan 2 nayaa roop maujood haye jaise kii 2-ayami modd gallois kaa pratinidhitva 2-ayami modd gallois key pratinidhitva key liye isomorphic haye. rebate kii pramey koo lagu karane key liye, yeh aparivartaniyata aur parinirdhaaran kii jaanch karane key liye paryaapt haye. tett vakr key siddhant kaa upayog karke, koee yeh saabit curr sakata haye kii yadi nyuntam bhedbhaav mein dikhaai dene vaali shakti koo vibhajit kartaa haye tou yeh aparimit aur seemit sapaat haye. taba rebate kii pramey kaa tatparya haye kii star kaa ack vajan 2 nayaa roop maujood haye.
star cumm karna.
rebate kii pramey bataati haye kii chaalak key ack dirghvrittakar vakr seey shuru honey seey star key ack dirghvrittakar vakr key astitva kii guaranti naheen milati haye. star key nae roop mein tarksangat fourier gunank naheen hoe sakate hain, aur isaliye yeh ack uchch-ayami abelian kism seey judaa hoe sakata haye, naa kii ack andakar vakr seey. udaaharan key liye, sameekaran dwara diye gaye cremona databases mein andakar vakr 4171a1
conductor aur discriminant key saath conductor 97 key ack andakar vakr key liye star-nimn modd 7 naheen haye. balki, modd gallois pratinidhitva star 97 key ack ataarkik nae roop key modd gallois pratinidhitva key liye samroop haye.
haalaanki, star-cumm nae roop key star kii tulanaa mein kaafee badey key liye, ack tarksangat nayaa roop (ee.jee. ack andakar vakr) koo ack anya tarksangat nae roop (ee.jee. andakar vakr). vishesh roop seey, ack tarksangat nae roop kaa modd gallois pratinidhitva star key ack ataarkik nae roop key liye samroop naheen hoe sakata haye.
isi tarah, free-majur anuman bhavishyavani kartaa haye kii paryaapt badey (chaalak seey swatantra) key liye, samroop modd gallois pratinidhitva key saath dirghvrittakar vakr vaastav mein samroop hain, aur isaliye ack hii chaalak haye. iss prakaar tarksangat nae roopon key beach gair-tuchchh star-ghataav badey paimaane parr honey kii bhavishyavani naheen kii gaee haye.
itihas.
unake shodh prabandh mein, ack alag ganitiya vastu key saath firmate key sameekaran key samadhan ("aeye", "bee", "see") koo jodane kaa vichaar utpann huaah ack dirghvrittakar vakr. yadi "p" ack visham abhaajya haye aur "a", "b", aur "c" sakaratmak purnank hain jaise kii
taba ack sambandhit free vakr sameekaran dwara diyaa gayaa ack beejganitiya vakr haye.
yeh sootra _ 2 parr paribhaashit genus ack kaa ack gair-ekal beejganitiya vakr haye, aur iska prakshepya puuraa honah sootra _ 2 parr ack dirghvrittakar vakr haye.
1982 mein gerhard free ney usee vakr key asamanya gunon kii or dhyaan aakarshit kiya, jise abb ack free vakr kahaa jaataa haye. yeh yeh darshaakar kii flt key liye ack counterexpal ack vakr banaayega joe modular naheen hoga, fermate aur taniyama key beach ack pull pradaan kartaa haye. iss anuman ney kaafee ruchi aakarshit kii jaba free ney sujhaav diyaa kii taniyama-shimura-weill anuman kaa arth haye flt. haalaanki, unakaa tark puuraa naheen thaa. 1985 mein jeane-piyare sair ney prastaav diyaa kii ack free vakr modular naheen hoe sakata haye aur ack aanshik pramaan pradaan kiya. isase pataa chalaa kii taniyama-shimura anuman key ardh-yogya mamle kaa pramaan flt kaa sanket dega. sair ney ack poorna pramaan pradaan naheen kiya aur laapata bitt koo apsilon anuman yaa ε-anuman key roop mein jaanaa jaane lagaa. 1986 kii garmiyon mein, keneth alaan rebate ney apsilon anuman koo saabit kiya, jisase yeh saabit huaa kii taniyama-shimura-weill anuman kaa arth thaa.
prabhaav.
maan leejiye kii ghatank key saath firmate sameekaran kaa samadhan gair-shoonya purnankon mein thaa. sambandhit free vakr ack dirghvrittakar vakr haye jiska nyuntam bhed barabar haye aur jiska chaalak i kaa moolank haye.ee. sabhi alag-alag avibhajya vibhajit kaa utpaad. sameekaran kaa ack praathamik vichaar, yeh spasht kartaa haye kii ack summ haye aur isaliye "aine" haye. taniyama-shimura anuman dwara, ack modular andakar vakr haye. choonki sabhi visham abhajyankon mein vibhajit honey vaale sabhi abhajyank nyuntam bhedbhaav mein ack shakti key roop mein dikhaai dete hain, rebate kii pramey punaraavritt star avrohan modulo dwara chaalak seey sabhi visham abhajyankon koo strip kiya jaataa haye. haalaanki, star 2 kaa koee nayaa roop naheen rahata haye kyonki modular vakr kaa vansh shoonya haye (aur star "aine" key nae roop bhinn hain.

