I Riemann mbono. Ukwabela amanani yinkulumbuso

Ngowe-1900, enye izazinzulu kakhulu kwinkulungwane yokugqibela, uDavid Hilbert wenza uluhlu eziquka iingxaki 23 engekasonjululwa lemathematika. Umsebenzi kubo iye yaba negalelo elikhulu kuphuhliso eli candelo ulwazi lwabantu. Emva kweminyaka eli-100 kwi-Clay Mathematical Institute thaca uluhlu lwe iingxaki ezisixhenxe, eyaziwa ngokuba neenjongo Millennium le. Kuba isigqibo nganye kuzo wanikela umvuzo $ 1 yezigidi.

Ingxaki kuphela, leyo phakathi izintlu ezimbini iiphazili, kangangeenkulungwane akazange abaphumze izazinzulu, waba hypothesis Riemann. Yena nangoku elinde ukuba isigqibo sakhe.

ulwazi Brief oluchaza

Georg Friedrich Bernhard Riemann wazalwa ngo-1826 e-Hanover, kwintsapho enkulu yomfundisi amahlwempu, yaye waphila iminyaka 39 kuphela ubudala. Wakwazi ukupapasha amaphepha-10. Nangona kunjalo, ngexesha ubomi Riemann Wakugqala ezihlangwini utitshala wakhe uJohann GAUSS. Eneminyaka eyi 25 isazinzulu oselula wayekhusela ithisisi yakhe "eziziziseko ezibalulekileyo thiyori imisebenzi esimbaxa variable." Kamva ke aliqulunqileyo hypothesis yakhe, abe nendumasi.

etsala

weza Mathematics xa umntu bafunda ukubala. Emva koko wavuka ingcamango yokuqala amanani, leyo kamva wazama lokuhlela. Kuye kwafunyaniswa ukuba abanye babo baye iipropati eqhelekileyo. Ngokukodwa, phakathi amanani zendalo m. E. Abo esetyenziswa ekubaleni (amanani) okanye inani elijongene lezinto zabelwe iqela ololo yahlulwe kuphela omnye ngokwabo. Babizwa ngokuba elula. An ubungqina ocacileyo theorem iseti engenasiphelo lwamanani anikwe Euclid ngo "Elements 'yakhe. Okwangoku, siqhubeka uphendlo lwabo. Ingakumbi, le likhulu inani owaziwa ² 74207281 - 1.

ifomula Euler kaThixo

Kunye nale ngcamango etsala ngamabona ezininzi Euclid ichazwe kwaye theorem wesibini factorization kuphela. Ngokutsho kuyo nayiphi kweqanda na imveliso enye kuphela iseti etsala. Ngowe-1737, sezibalo waseJamani omkhulu Leonhard Euler wavakalisa yokuqala theorem Euclid ngalo Infinity lwe kwifomula eboniswe ngezantsi.

Ibizwa ngokuba umsebenzi zeta, apho s - a rhoqo kwaye p ke onke amaxabiso elula. Ukusuka ulandele ngqo kunye nokuvunywa yokukhetheka ukwanda Euclid.

Riemann zeta umsebenzi

formula Euler ukuba uhlolo sihlolisisa Kuyinto ephawulekayo, njengoko inikelwa umlinganiselo phakathi elula integers. Ngapha koko, ecaleni lakhe lasekhohlo luyanda amabinzana ngamabona ezininzi ezixhomekeke ezilula kuphela, kunye nelungelo mali lu dityanisiwe zonke integers ezintle.

Riemann waqhubeka Euler. Ukuze ufumane iqhosha le ngxaki ukwahlulelana amanani, kucetywa ukuba ukuchaza Ifomula zombini umahluko wokwenene ezintsonkothileyo. Yaba yena lowo kamva yabizwa ngokuba Riemann zeta umsebenzi. Ngo-1859 i sisazinzulu wapapasha inqaku elinomxholo othi "Xa inani etsala ukuba ingadluli ixabiso kwangaphambili", nto leyo ushwankathelwa zonke iingcamango zabo.

Riemann ecetywayo ukusetyenziswa inani Euler, convergent kuzo zonke s lenene> 1. Ukuba fomula inye isetyenziselwa s ezintsonkothileyo, ngoko ke manqaku aya idibane nayiphi na ixabiso variable kunye yinxalenye mkhulu 1. Riemann wasebenzisa ukuqhubeka zicazulule inkqubo ngokuthi kwandiswe kwinkcazelo zeta (s) kuwo onke amanani ezintsonkothileyo, kodwa 'ilahle "unit. Kwakungekho lula, kuba xa s = 1 umsebenzi zeta ukunyuka ukuya yokungapheli.

ingqondo practical

Umbuzo umbuzo: yintoni na umsebenzi zeta umdla yaye kubalulekile, nto leyo ebaluleke kakhulu kumsebenzi Riemann kwi hypothesis null? Njengoko usazi, ngomzuzu akafunyanelwanga ipateni elula elichaza ukwabiwa amanani yinkulumbuso phakathi zendalo. Riemann sikwazi ukubona ukuba inani PI (x) lweenombolo inkulumbuso, izinto ezo kunabanye x, kubonakaliswa ukwabiwa nontrivial umsebenzi zero zeta. Ngaphezu koko, hypothesis Riemann yimeko kuyimfuneko ukuze ukungqina iimvavanyo ubuchule ezithile lokufihla okwethutyana.

I Riemann hypothesis

Enye imixube yokuqala yale ngxaki zezibalo, hayi ukuwuphumeza kule mini, le: ingenamsebenzi umsebenzi 0 zeta - amanani ezintsonkothileyo inxalenye yokwenene elingana ½. Ngamanye amazwi, ukuba zicwangciswe kumgca othe ngqo Re s = ½.

Kukho kwakhona Riemann hypothesis nolahlo ngokubanzi, nto leyo nkulumo, kodwa gabalala le zeta-imisebenzi, ezo zibizwa ngokuba Dirichlet (bona. Ifoto ngezantsi) L-imisebenzi.

Xa χ ifomula (n) - umlinganiswa lwamanani (k mod).

mazwi Riemann yeyona ekuthiwa hypothesis null, njengoko iqinisekisiwe malunga nokungqinelana nomGaqo-data isampula ekhoyo.

Njengoko Ndamphikisa Riemann

Qaphela yezibalo German ukuba ekuqaleni zavela kakhulu uzifunda. Inyaniso kukuba ngelo xesha sisazinzulu wayesiya ukuze angqine theorem kwi ukwabiwa amanani inkulumbuso, kwaye kule meko, oku hypothesis akanayo ukusebenza kakhulu. Nangona kunjalo, indima yayo ekulungiseni eminye imiba emininzi yeyabahlali. Kungenxa yoko le nto hypothesis Riemann kuba ngoku izazinzulu ezininzi ingqalelo ebalulekileyo iingxaki bokuba zezibalo.

Njengokuba kuthiwe, ubungqina theorem ekusasazweni ngokupheleleyo Riemann hypothesis ayikho kuyimfuneko, kwaye enengqondo zingqina ukuba yinxalenye yazo naziphi non-engenamsebenzi zero lo msebenzi zeta liphakathi kuka-0 no 1. Le ndawo ithetha ukuba udibaniso lwamaxabiso wonke 0-m umsebenzi zeta ezivelayo kule formula ngqo ngasentla, - ezisikelwe rhoqo. Kuba amaxabiso elikhulu x, oko konke kulahleka. Ilungu kuphela olungumgubo, nto leyo iya kuhlala injalo de kwi x eziphakamileyo kakhulu, x ngokwakhe. Ezinye ngokwemigaqo ezintsonkothileyo kuthelekiswa nayo shwaka asymptotically. Ngenxa yoko, isixa evavanyiweyo uyabaleka x. Le yobunyani kuqwalaselwa njengobungqina inyaniso yinkulumbuso Inombolo theorem. Ngenxa yoko, amaqanda lomsebenzi Riemann zeta kubonakala indima ekhethekileyo. Kuyinto ukungqina ukuba ezi amaxabiso abakwazi negalelo elibonakalayo wokubala ukwanda.

abalandeli Riemann

Ukufa kabuhlungu ukusuka tuberculosis kuthintele nzulu bazise ekupheleni ubhalo le program. Noko ke, wathabatha ikhuni evela W-F. de la Vallée Poussin kunye Zhak Adamar. Ngokuzimeleyo ngalinye ezinye beshenxile yinkulumbuso theorem inani. Hadamard kunye Poussin wakwazi ukungqina ukuba wonke umsebenzi 0 zeta nontrivial ibekwe ngaphakathi band ezibalulekileyo.

Ngenxa umsebenzi kwezi izazinzulu, isebe elitsha lemathematika - theory okuhlalutya amanani. Kamva, abanye abaphandi baye bafumana kancinane ubungqina abangekaphuhli nangaphezulu theorem wayesebenza eRoma. Ngokukodwa, Pal Erdös kunye Atle Selberg ndiwuvulile nokuba esiqinisekisa ikhonkco yayo entsonkothileyo kakhulu ekuqiqeni, hayi kufuna ukusetyenziswa uhlalutyo ezintsonkothileyo. Noko ke, ngeli xesha ingcamango Riemann ngu theorems ezininzi ezibalulekileyo ekungqiniweyo, kuquka isilinganiselo imisebenzi emininzi kwethiyori inani. Malunga nalo msebenzi omtsha Erdős kunye Atle Selberg phantse nantoni ayiphazamiseki.

Enye ubungqina ilula kwaye eyona intle le ngxaki sele uyifumene 1980 yi uDonald Newman. It lusekelwe Cauchy theorem ezaziwayo-kakuhle.

Ezisengozini ukuba hypothesis Riemann yeyona sisiseko ufihlo lwangoku

encryption Data yavela kunye ukubonakala abalinganiswa, hayi kanye mandithi, bona ngokwabo oya kuthathwa njengomntu ikhowudi yokuqala. Okwangoku, kukho isimo esitsha wonke ufihlo yedijithali, nto leyo inxaxheba kuphuhliso ubuchule ufihlo.

Elula "Semisimple" inombolo m. E. Abo yahlulwe kuphela kwezinye amanani amabini kwiklasi enye, asisiseko kwinkqubo karhulumente ephambili, eyaziwa ngokuba RSA. It has a isicelo ngokubanzi. Ngokukodwa, lisetyenziswa kwi isizukulwana i yogesi. Ukuba sithethe ngokoMthetho "teapot 'ekhoyo, hypothesis Riemann eyithethayo ubukho inkqubo ukwabiwa yamanani yinkulumbuso. Ngenxa yoko, kakhulu kuncitshiswa ukumelana yezitshixo icryptographic, apho kuxhomekeke kukhuseleko kwiintengiselwano Intanethi e-kwezorhwebo.

Ezinye iingxaki engekasonjululwa zezibalo

Zalisa nqaku kubalulekile nikela amagama ambalwa eminye imisebenzi kule nkulungwane. Ezi ziquka:

• Ukulingana kweeklasi P NP. Le ngxaki uqulunqe ngolu hlobo lulandelayo: Ukuba impendulo omhle kumbuzo enikwe iqinisekiswa ngexesha polynomial, ke kuyinyaniso ukuba yena impendulo yalo mbuzo ifumaneka ngokukhawuleza?
• Hodge liyavumelana. Ngamazwi alula kokuba kuchazwe ngolu hlobo lulandelayo: kuba ezinye iintlobo manifolds projective aljibra (izithuba) Hodge imijikelo ezi indibaniso yezinto ukuba abe ukutyhilwa zejometri, okt imijikelo algebra ...
• liyavumelana Poincaré. Yiyo kuphela ubungqina bokuba iingxaki mzuzu kwiwaka. Ngokutsho kuyo nayiphi na into-ntathu ukuba iimpawu ezithile kwisigaba-3 mbini, kwisigaba sikarhulumente kufuneka echanekileyo deformation.
• Ukwamkelwa umyinge Yang - mbono Mills. Kufuneka ukuba ukungqina ukuba ithiyori quantum, wabeka phambili ngala izazinzulu ukuya isithuba R ^4, kukho isiphako 0-mass nawuphi na umlinganiselo kwimibhobho elula zeqela compact G.
• Hypothesis ye Birch - Swinnerton-Dyer. Le yenye ingxaki ezifanele zokufihlakeleyoComment. Noko ke amagophe okweqanda.
• Ingxaki ubukho kunye ngobuqhophololo izisombululo ye Navier - kwizibalo Stokes.

Ngoku uyazi i Riemann hypothesis. Ngamagama alula, siye saqulunqwa kwaye ezinye iinjongo kwiwaka. Isibakala sokuba baza isonjululwe okanye kuvunyiwe ukuba akukho isisombululo - ukuba lo mbandela ixesha. Kwaye oku akulindelekanga ukuba kufuneka ulinde ixesha elide kakhulu, njengoko imathematika baya bezisebenzisa amandla azo kuzo iikhompyutha. Noko ke, yonke into ixhomekeke ngobugcisa ukusombulula iingxaki zenzululwazi kakhulu kufuna intuition kunye nobuchule.