bernsideche pramey

ganitachya gut siddhantatil bernsideche pramey asey sangate qee jarr 'g' haah kram sootra _ 1 chaa maryadit gut asel jethe 'p' aanee 'q' yaa abhajya sankhya asateel aanee 'a' aanee 'b' heey nakaratmak nasalele purnank asateel, tarr 'g' sodavata yenyajoga asel. tyamule pratyek
naun-abelian maryadit sadhya gatacha kram kiman teen bhinn avibhajyanni vibhajya asato.
itihas.
maryadit gatanchya pratinidhitva siddhantacha vapar karoon heey pramey siddha jhaale. yaa siddhantachi anek vishesh prakarane bernside, jorden aanee frobenius yanni yapurvi siddha kelee hotee. johnn thompson yanni nidarshanas aanoon dile qee pratinidhitva siddhantacha vapar talhanara purava aine-gut prameyavaril tyanchya karyatoon kadhala jaau shakato aanee heey spashtapane visham kramachya gatansathi aanee summ kramachya gatansathi kele gele hote. purave sope kele.
purava.
khaleel purava-bernsidepeksha adhik parshvabhoomicha vapar karane-virodhabhasane aahe. pakb' haah done abhajya shaktincha sarvat lahan gunakar asoo dya, mhanje eka nirakaran naan karata yenara gut 'jee' aahe jyachi kramvari yaa sankhyechya barobarichi aahe.
jarr 'jee' madhye 'etch' haah kshullak nasalela yogya samanya upasamuh asel, tarr ('jee' chya kimanatemule), 'etch' aanee 'jee'/'etch' sodavata yenyajoge asateel, tyamule 'jee' dekhil, jeey aaplya gruhitakachya viruddha asel. tyamule 'jee' sope aahe.
jarr "a" shoonya asel, tarr g haah eka maryadit q-gut asel, tyamule too nirgunak asel aanee tyamule too sodavata yeil.
tyachpramane, "jee" heey abelian asoo shakat nahee, anyatha teey sodavata yenyajoge asel. jee" heey sope asalyane, tyache kendra kshullak asale pahije.
sayalochya prameyatil pahilya vidhananusar, 'jee' madhye 'pii' kramacha 'ess' upasamuh aahe. kaaran "s" haah eka alpasankhyak nasalela "p"-gut aahe, tyacha kendrabindu "z" ("s") alpasankhyak nahee. kshullak ghatak sootra _ 2 nishchit qaraa. 'jee' chya sanyugmakanchi sankhya tyachya sthirikaran upasamuh 'jeejee' chya nirdeshankaitaki asate, jee 'ess' chya nirdeshank 'cubie' laa vibhajit karate (kaaran 'ess' haah 'jeejee' chaa upasamuh aahe). tyamule hii sankhya 'qd' chya rupat aahe. shivay, purnank 'dii' katekorpane sakaratmak aahe, kaaran 'jee' haah kshullak nahee aanee mhanoon 'jee' madhye madhyavarti nahee.
("χ" i ") 1 ≤" i "≤" h "heey sootra _ 3 varr" g "chya aparivartaniy varnanche kutumb asoo dya (yethe" χ "1 heey kshullak varn darshavate). kaaran "g" haah 1 chya samaan sanyugmata vargat naslyamule, gatachya varn saranichya stambhansathi orthogonality sambandh detoh
aata 'χ' i '(' g ') heey bijganitiy purnank aahet, kaaran teey ektechya mulanchi berries aahet. g" varr nahishi naan honari serve alpamoolyaheen irreducible akshare 1 varr "q" neey vibhajya moolya ghetalyas, aapan asey gruheet dharato qee
haah eka bijganitiy purnank aahe (kaaran too bijganitiy purnankanchya purnank gunankanchi berries aahe), joou nirathak aahe. heey vidhan siddha karate.
g", "z" (sootra _ 6 ["g"]) vareel purnank-moolya varg karyancha sanch, eka parivartaneey ring aahe, jee sootra _ 6 varr maryaditpane tayar hote. tyache serve ghatak asha prakare sootra _ 6 varr avibhajya aahet, visheshtah mapping "u" jeey g chya sanyugmata vargavar 1 aanee itaratra 0 moolya ghete.
mapping sootra _ 9 jeey varg karya "f" pathavate
eka ring homomorphism aahe. kaaran serve 's' sathee 'ρ' ('s') −1 'a' ('u') 'ρ' ('s') = 'a' ('u'), mhanoon 'a' ('u') haah samarupata λin aahe asey shurcha shabdalekhan soochit karato. tyacha trace "nλ" barobar aahe
kaaran samarupata 'λi' n 'hii avibhajya ghatakachi samaroop pratima aahe, tyamule heey siddha hote qee jatil sankhya' λ '=' q 'd' χ '(' g ')/' n 'hii eka bijganitiy purnank aahe.
q" haah "n" chaa tulanene avibhajya asalyane, bezoutchya olakhinusar "x" aanee "y" asey done purnank aahet keeh
kaaran bijganitiy purnankanchya purnank gunankansah resheey sanyojan punha eka bijganitiy purnank aahe, heey vidhan siddha karate.
ζ" hii "χ" ("g")/"n" hii jatil sankhya asoo dya. haah eka bijganitiy purnank aahe, mhanoon tyacha manak "n" ("ζ") (i.eae. tyachya sanyugmanche gunakar, mhanje sootra _ 13 vareel tyachya kiman bahupadichi mule) haah eka shunyetar purnank aahe. aata 'ζ' hii ektechya mulanchi sarasari aahe ('ρ' ('g') chee eigenvalues), mhanoon tyache sanyugma aahet, mhanoon tyaa sarvanche nirpeksh moolya 1 peksha qamee kinwa samaan aahe. kaaran tyanchya utpadanache 'n' ('ζ') heey nirpeksh moolya 1 peksha jaast kinwa samaan aahe, tyanche nirpeksh moolya serve 1 asane aavashyak aahe, visheshtah 'ζ', jyacha arth assa aahe qee 'ρ' ('g') chee eigenvalues serve samaan aahet, mhanoon 'ρ' ('g') hii eka samarupata aahe.
n' haah 'ρ' chaa curnell asoo dya. samarupata "ρ" ("g") hii "im" ("ρ") madhye madhyavarti aahe (jee "g"/"n" sathee samaroop aahe), tarr "g" hii "g" madhye madhyavarti nahee. parinami, sadhya gut 'jee' chaa samanya upasamuh 'aine' haah kshullak nahee, mhanoon too 'jee' chya barobaricha aahe, joou ρ heey kshullak pratinidhitva nahee yaa vastusthitishi virodhabhas darshavito.
haah virodhabhas heey pramey siddha karato.

