I Riemann Hypothesis. Ukusatshalaliswa izinombolo eziyinhloko

Ngo-1900, omunye ososayensi kunabo bonke ekhulwini elidlule, uDavide Hilbert wenza uhlu ehlanganisa 23 izinkinga ezingaxazululeki wezibalo. Umsebenzi kubo liye laba nethonya elikhulu ekuthuthukiseni le nkambu bolwazi lwabantu. Ngemva kweminyaka engu-100 e-Clay Mathematical Institute owethulwe uhlu lwezinkinga eziyisikhombisa, eyaziwa ngokuthi izinhloso Eyinkulungwane. Ukuze isinqumo ngamunye kubo wanikelwa umklomelo ka- $ 1 million.

Inkinga kuphela, okuyinto kwaba phakathi izinhlu ezimbili puzzle, kwaphela amakhulu eminyaka enganikanga ukuphumula ososayensi, waba Riemann hypothesis. Namanje elinde isinqumo sakhe.

Imininingwane emfushane umlandvomufi

Georg Friedrich Bernhard Riemann wazalwa ngo 1826 e Hanover, emkhayeni omkhulu umfundisi abampofu, futhi wahlala iminyaka 39 kuphela ubudala. Wakwazi ukushicilela 10 amaphepha. Nokho, ngesikhathi impilo Riemann wayebheka umuntu owayezothatha isikhundla uthisha wakhe Johann Gauss. Lapho ngineminyaka engu-25, usosayensi abasha bavikela mqondo yakhe "Izikhwama inkolelo-mbono yokuziphendukela imisebenzi kwenombolo eziyinkimbinkimbi." Kamuva lapho zavela hypothesis wakhe, okuyinto eyaduma.

primes

Mathematics lapho indoda efundile ukubala. Yayisisuka umqondo wokuqala izinombolo, okuyinto kamuva wazama zokuhlukanisa. Kuye kwaphawulwa ukuthi ukuba abanye kubo bacele izakhiwo ezivamile. Ikakhulukazi, phakathi izinombolo yemvelo m. E. Labo ayesetshenziselwa kulesi sibalo (izinombolo) noma inombolo eziqokiwe izinto kwabelwe iqembu enjalo okuyinto zihlukaniswe kuphela ngomunye futhi ngokwabo. Babizwa ngokuthi elula. Kuvele ubufakazi nenhle of theorem isethi okungenamkhawulo izinombolo eyanikezwa Euclid e "Imisuka" yakhe. Okwamanje, siyaqhubeka nosesho lwabo. Ikakhulu, i-elikhulu eziningana ezaziwayo ² 74207281 - 1.

ifomula Euler

Kanye lo mqondo primes ngokungenamkhawulo eziningi Euclid kuchazwa futhi theorem wesibili kungenzeka factorization kuphela. Ngokusho ke iyiphi inombolo ephelele engaphezulu kweqanda iwumkhiqizo eyodwa kuphela iqoqo primes. Ngo-1737, isazi sezibalo esikhulu German Leonhard Euler uzwakalise lokuqala theorem Euclid sika phezu infinity formula kukhonjisiwe ngezansi.

Ibizwa ngokuthi umsebenzi Zeta, lapho ama - njalo futhi p kuyinto wonke amanani elula. Kusukela ke balandela ngqo nokuvunywa ohlukile ukunwetshwa Euclid.

Riemann Zeta umsebenzi

ifomula Euler ku sihlolisisa Kuyinto ephawulekayo ngempela, njengombana sinikelwa lihlela isilinganiso phakathi kwama elula integers. Phela, uhlangothi lwesobunxele ziziningi izinkulumo ngokungenamkhawulo eziningi encike kuphela elula, futhi ngesilinganiso esifanele lihlotshaniswa zonke integers omuhle.

Riemann waqhubeka Euler. Ukuze uthole ukhiye lenkinga ukusatshalaliswa izinombolo, kuphakanyiswa ukuchaza ifomula kokubili variable yangempela futhi eziyinkimbinkimbi. Kwaba esona kamuva waziwa ngokuthi Riemann Zeta umsebenzi. Ngo-1859 usosayensi yashicilela isihloko esithi "Kuyi-inani primes ukuthi musa kwinani predetermined", okuyinto wafingqa yonke imibono yabo.

Riemann ezihlongozwayo ukusetshenziswa eziningana Euler, convergent kuwo wonke ama real> 1. Uma indlela efanayo isetshenziselwa s eziyinkimbinkimbi, ngakho-ke chungechunge sizophendula bukhomba nganoma yisiphi ukubaluleka variable ngengxenye real mkhulu kunezinhliziyo 1. Riemann esetshenziswa ukuqhubeka ahlaziye inqubo ukhulisa kwencazelo Zeta (s) zonke izinombolo eziyinkimbinkimbi, kodwa "uphonsa" iyunithi. Kwakungenakwenzeka, ngoba uma s = 1 Zeta umsebenzi inyuka infinity.

ngomqondo ongokoqobo

Lo mbuzo ubuzwa: yini Zeta umsebenzi ezithakazelisayo futhi ebalulekile, okuyinto ebalulekile emsebenzini Riemann ku umbono null? Njengoba wazi, okwamanje akatholakali iphethini lelula echaza ukusatshalaliswa izinombolo eziyinhloko phakathi zemvelo. Riemann sikwazi ukuzwa ukuthi isibalo pi (x) izinombolo prime, engesiyo njengoba kuphakeme kakhulu x, uwukubonakaliswa ukusatshalaliswa nontrivial zero Zeta umsebenzi. Ngaphezu kwalokho, umbono Riemann yisimo ezidingekayo ukuze afakazele okuhlaziya yesikhashana algorithm ethile cryptographic.

I Riemann hypothesis

Omunye ukwakhiwa lokuqala le nkinga zezibalo, hhayi kungase kutholakale kuze kube yilolu suku, yilesi: eziwubala 0 Zeta umsebenzi - eqela nge real okuyingxenye elilingana ½. Ngamanye amazwi, benza ahlelwe emgceni locondzile Re s = ½.

Kukhona generalized Riemann hypothesis, okuyinto leyo nkulumo, kodwa nje okungaqondile we Zeta-imisebenzi, ezibizwa ngokuthi i-Dirichlet (bheka. Photo ngezansi) L-imisebenzi.

Esikhathini χ ifomula (n) - uhlamvu zezinombolo (k Mod).

isitatimende Riemann iyona okuthiwa null hypothesis, njengoba sekuqinisekisiwe ngoba ukungaguquguquki ngedatha ekhona isampula.

Njengoba Nga- ngibatshela Riemann

Qaphela sezibalo German ekuqaleni zavela ngempela zokuphola. Iqiniso liwukuthi ngaleso sikhathi usosayensi wayehamba ukufakazela i ifayela echaza ifomu ku ukusatshalaliswa izinombolo eziyinhloko, futhi kulo mongo, lo mbono akanayo effect okuningi. Nokho, indima yayo ekhuluma nezinye izindaba eziningi nawo njengomnyango mkhulu kakhulu. Yingakho Riemann hypothesis okwamanje ososayensi abaningi bayasiqaphela ebalulekile izinkinga unproven zezibalo.

Njengoba kuye kwashiwo, ukufakazela theorem ku ukusatshalaliswa ngokugcwele Riemann hypothesis akudingekile, futhi enengqondo ukufakazela ukuthi ingxenye yangempela okungebona eziwubala-zero umsebenzi Zeta kuyinto kuka-0 no 1. Lokhu impahla kusho ukuthi isamba sazo zonke 0-m Zeta umsebenzi avele ifomula ngqo ngenhla, - ezilinganiselwe njalo. Ukuze amagugu enkulu x, kungaba zonke izolahleka. UKhoza, onguyena kuphela formula, okuzokwenza zihlala zinjalo ngisho at x eliphezulu kakhulu, x yena. Zonke ezinye imigomo eziyinkimbinkimbi, uma kulinganiswa nokwenu ke asymptotically zinyamalale. Ngakho, isamba kwesamba ivame ukuba x. Leli qiniso kungaba kubhekwe njengobufakazi bokuthi iqiniso inombolo esiyinhloko theorem. Ngakho, amaqanda umsebenzi Riemann Zeta livela indima ekhethekile. Kuyinto ukufakazela ukuthi lamagugu hhayi kungamsiza kakhulu ukuba le formula ukunwetshwa.

Riemann abalandeli

Ukufa kabuhlungu sofuba uvinjelwe usosayensi ukuletha kuze kube sekupheleni okunengqondo zohlelo. Nokho, wathatha baton kusukela W-F. de la Vallee Poussin futhi Zhak Adamar. Ngayodwana base kuhoxiswe inombolo esiyinhloko theorem. Hadamard futhi Poussin bakwazi ukufakazela ukuthi zonke nontrivial 0 Zeta umsebenzi zitholakala ngaphakathi band ezibucayi.

Ngenxa yalo msebenzi lezi ososayensi, igatsha elisha wezibalo - theory kohlaziyo izinombolo. Kamuva, abanye abacwaningi baye bathola ubufakazi kancane bakudala ngaphezulu theorem bekasebenza eRoma. Ikakhulukazi, Pal Erdös futhi Atle Selberg aye aboniswa eqinisekisa chain yayo eziyinkimbinkimbi kakhulu logic, asidingi ukusetshenziswa ukuhlaziywa eziyinkimbinkimbi. Nokho, kuleli qophelo umbono ka Riemann ngu theorems ezibalulekile eziningana eziye kungase kutholakale, kuhlanganise isilinganiselo imisebenzi eminingi inombolo theory. Ngokuqondene nalokhu umsebenzi omusha Erdős futhi Atle Selberg cishe yonke into ayiphazamiseki.

Omunye ubufakazi elula futhi enhle kakhulu le nkinga Kuye kwatholakala 1980 by Donald Newman. Yayisekelwe kuyi-Cauchy theorem owaziwa.

Sisengozini uma hypothesis Riemann sika ngesisekelo indlela yokubhala efihla incazelo yesimanje

Ukubethelwa kwedatha sekukhona nge ukubukeka izinhlamvu, noma kunalokho, bona ngokwabo kungabhekwa njengokwenzeka ikhodi kuqala. Okwamanje, kukhona umkhuba omusha yonke indlela yokubhala efihla incazelo digital, okuyinto waziphatha ukuthuthukiswa ukubethela algorithm.

Simple futhi "Semisimple" inombolo m. E. Labo zazo kuphela ihlukaniswe ezinye izinombolo ezimbili kulelo kilasi, ziyisisekelo uhlelo kokhiye, eyaziwa ngokuthi i-RSA. It has a isicelo ebanzi. Ikakhulu, isetshenziswa isizukulwane i yogesi. Uma sikhuluma ngokoMthetho "teapot" atholakalayo, umbono Riemann ehlola khona kohlelo ukusatshalaliswa izinombolo eziyinhloko. Ngakho, kakhulu ziyancipha ukumelana okhiye cryptographic, lapho kuncike ukuphepha nakuyi-Internet e-e-commerce.

Ezinye izinkinga ezingaxazululeki zezibalo

Gcwalisa sihloko kuwufanele nikela amagama ambalwa eminye imisebenzi weminyaka eyinkulungwane. Lezi zihlanganisa:

• Ukulingana amakilasi P no NP. Inkinga is washayelwa kanje: uma impendulo omuhle ukuba umbuzo inikezwe liqinisekisiwe ngesikhathi polynomial ke ingabe kuyiqiniso ukuthi yena ngokwakhe impendulo yalo mbuzo ingatholakala ngokushesha?
• Hodge conjecture. Ngamagama alula kungashiwo kushiwo kanje: ezinye izinhlobo zama-projective manifolds algebraic (izikhala) Hodge imijikelezo kukhona inhlanganisela yezinto abe incazelo weJiyomethri, okusho imijikelezo algebraic ...
• conjecture Poincaré. Kuyinto kuphela kungase kutholakale izinkinga okwamanje yeminyaka. Ngokusho kwalo kunoma iyiphi into ngakuthathu kokuba izakhiwo ezithile emkhakheni 3-ntathu, ezinhlakeni kumele kube enembile ukusonteka.
• Ukuvunywa quantum Yang - Mills theory. Sidinga ukufakazela ukuthi imfundiso quantum, abeke phambili yilezi ososayensi ukuba isikhala R ^4, kunesici 0-mass nganoma yisiphi Samandla okulula iqembu compact G.
• Umbono we Birch - Swinnerton-Dyer. Lena enye inkinga ukuthi lubalulekile Cryptography. Kumayelana Curves okweqanda.
• Inkinga ye-khona kanye olubushelelezi izisombululo we Navier - Stokes zibalo.

Manje wazi Riemann hypothesis. Ngamagama alula, siye zavela futhi ezinye izinjongo weminyaka eyinkulungwane. Iqiniso lokuthi ngeke ixazululwe noma kunobufakazi bengenanto isixazululo - kungcono Kuxhomeke isikhathi. Futhi lokhu kubonakala kungeke kudingeke ukuba ulinde isikhathi eside kakhulu, njengoba izibalo ziya ziba mandla ekusebenziseni amandla azo lwamakhompyutha. Nokho, akukhona konke kungaphansi ubuciko ukuxazulula izinkinga yesayensi ngokuyinhloko kudinga umuzwa kanye nobuchule.