
theetta devisor

ganithashaasthrathil, theetta divisar θ ennathu beejaganita jyaamithiyude ardhathil sankeernna samkhyakalkku (pradhaanamaayum dhruveekarikkapetta) mukalilulla abelian inam "a" ll nirvachichirikkunna anubandha reeman theetta-functionte seero locus kondu nirvachikkapetta oru bhajakamaanu. athinaal ithu mangiya alavil "a"-1 nte beejaganita upavibhagamaanu.
classical sidhaantham.
bernhard reemante classical phalangal θ-yeei mattoru vidhathil vivarikkunnu, "a" ennathu oru beejaganita vakrathinte (compact reeman uparithalam) "c" yude jacobian inamaaya "j" aanu. c" yill adisthaana pooyint "p" thiranjedukkunnathinu, digri 0-leeii "c"-leeii bhaajakangalude rekheeya thulyatha klaasukalaayi "j" enna vyaakhyaanathiloode "c" muthal "j" vareyulla oru staanderd mapping undu. athaayath, "c"-leeii "q" mapp "q"-p "classilake mapp cheiyunnu. jeey" oru beejaganita grooppaayathinaal, "sii" "yeei" jeey "yill" keey "thavana cherkkaam, ithu" dablyu "" keey "enna upavibhaagangalkk kaaranamaakunnu".
g" ennathu "c" yude janussaanengil, "w" "g" −1-nte "j"-ll θ oru vivarthanamaanennu riman theliyichu. "w" "g" −1-leeii eathu poyintukalaanu noonn-singular ennum addeham vivarichu avaa sthiraamkangal ozhikeyulla anubandha meromorphic fangshanukalonnumillaathu digri "g" −1-nte phalapradamaaya divaisarukalumaayi "d" poruthappedunnu. kooduthal classical bhashayil, eee "dii" oru sthiramallaatha functionte dhruva bhaajakathil aadhipathyam pularthunnilla enna ardhathil "sii" yill vibhaajakangalude oru rekheeya samvidaanathil neengunnilla.
d" aadipathyamulla pooll devisor ulla leanierly indipendant meromorphic functionukalude ennamaayi "d" allengil "h" 0 (o ("d")) ennathinu thulyamaayi "c" yill cartier devisoraayi "d" maayi bandhapetta holomorphic line bundle leanierly indipendant global sekshanukalude ennamaayi "w" g "−1-ll" p "= klaas (" d ") enna pooyintinte gunithathe thiricharinju kondu riman singulaaritti sidhaantham veendum theliyichu.
pinneedu jolie.
1973ll jorjju kempf, david mumfordinteyum andreotti meyarinteyum pravartthanatthe adisthaanamaakki, 1 ≤ "k" ≤ "g" −1 ennathinu "w" k "ennathil" p "= klaas (" d ") pooyintukalude singulaarittikalude vivaranathilekku" riman singulaaritti sidhaantham "vipuleekarichu. prathyekichum" d "(riman-kempf singulaaritti sidhaantham) maayi bandhapetta swatantra meromorphic functionukalude ennathinte adisthaanathilum addeham avayude gunithangal kanakkakki.
kooduthal krithyamaayi paranjaal, kmpf "h" 0 (o ("d")) kanakkaakkunna krithyamaaya shreniyil ninnu varunna maatriksukalude oru kudumbatthilekku "p" nuu sameepam praadeshikamaayi "j" mapp cheythu, "w" k "paramavadhi rankil thaazheyulla maatriksukalude lokkasumaayi poruthappedunna vidhathil. gunitasheshi appol anubandha rank lokkasile pooyintumaayi yojikkunnu. vyakthamaayi paranjaal
classil ("d") "w" k "yude gunanam binomial coffificient aanu.
k" = "g" −1 aayirikkumbol, ithu "r" + 1 aanu, rimante soothravaakyam.