Ka Riemann Ke Kuhiakau. Hoi o ka makana o ke Kuhina Nui helu

I ka 1900, kekahi o nā kānakaʻepekema nui loa o ka hope ke kenekulia, David Hilbert i ka papa inoa iloko olaila 23 unsolved pilikia o makemakika o. E hana ma luna o ia ua i ka weliweli no hopena ma luna o ka ulu o keia kahua o ke kanakaʻike. 100 makahiki i loko o ka Clay makemakika Institute ma hope hooku iho la ia i ka papa inoa o nā pilikia, ike e like me ka Ka Wā Kaukani Pahuhopu. No ka hooholo ana o kela mea keia mea o lakou i kaumaha aku i ka makana o $ 1 miliona.

Ke wale pilikia, a i waena o na kahua elua o ka puzzles, no ka kenekulia i ole haawi koena i kaʻepekema, lilo iho la ka Riemann kuhiakau. Ua ua nō e kali ana no kona hooholo ana.

Pōkole biographical 'ike

Georg Friedrich Bernhard Riemann i hānau i loko o 1826 ma Hanover, ma ka ohana o ka nui o ka poe ilihune kahu hipa, a ua noho wale nō 39 makahiki. He hoʻokele e hoolaha 10 pepa. Eia naʻe, ma ka ola o Riemann aole ia i manao i ka hope o kana kumu Johann Gauss. Ma makahiki 25 ui nä känaka 'epekema kokua aku i kona ia hoʻi "kumu o ka pähola' ana o mana o ka luna 'ee iaaanu aey." Hope aku la ua kālaiʻia i kona kuhiakau, a lilo kaulana.

primes

Makemakika hele mai ka wā kanaka aʻo i ka helu. A laila, kū aʻela i ka mua manaʻo o nā huahelu, a ma hope ho'āʻo e classify. Ua Ua ua ike ia kekahi o ia i na waiwai. Ma 'ana, i waena o ka mea maoli huina m. E.ʻO i i hoʻohana' ia ma o ka i ka ho omaulia (helu) a me ka i koho helu o nā 'ikamu i ua anao? Aou i ka pae ana o ia a i puunaueia wale e kekahi a me lakou iho. Ka mea, i kapaʻia poe noonoo ole. An leo hone hooiaio o ka theorem aloha 'ia paha o nā helu i haawiia e Euclid ma o kona "hehee wale". I ka manawa, ua e mau lākou huli 'ana. Ma 'ana, me ka nui o ka helu ana i ike ² 74207281 - 1.

Euler ka haʻilula

A me ka manaʻo o infinitely nui primes Euclid i ho'ākāka 'a me ka lua o ka theorem ka wale e hiki factorization. E like me ka mea, i kekahi maikaʻi helu o ka huina hoonui o kekahi wale 'ia paha o nā primes. I ka 1737, o ka nui Kelemānia mathematician Leonhard Euler hōʻike mua o ko Euclid ka theorem ma ka infinity o ka haʻilula i hoikeia ma lalo nei.

Ua Ua kapaʻia ka zeta papa, kahi mau - he mau a me ka pa mea a pau na mea Hawaiʻi. Mai ka mea, ma kahi e hahai a me ka apono ana o ke kū hoʻokahi o ke anoe o Euclid.

Riemann zeta kuleana pili i

Euler ka haʻilula ma luna o ka pilina nana ka loa kamahaʻo, i hāʻawiʻia mai ma ka lākiō ma waena o ka poe noonoo ole a me ka integers. Ma hope o nā mea a pau, i loko o konaʻaoʻao hema i hoonuiia infinitely nui, ka 'aoʻao e hilinai wale ana ma na mea, a ma ke dala akau ua pili i nā mea a pau maikaʻi integers.

Riemann hele aku ma Euler. I mea e imi i ke ki i ka pilikia o ka puunaue ana o ka helu, ka mea, ua manaoia e hoakaka i ka haʻilula no nā ka oiaio a me ka luna 'ee iaaanu aey. Ka mea, ua iho la ka mea hope i kapa e like me ka Riemann zeta kuleana pili i. I ka 1859 i ke nä känaka 'epekema paʻi ka' atikala ia "Ma ka helu ana o primes i mai i oi aku i ka hoʻoholo ma mua waiwai", i summed mai a pau kā lākou mau manaʻo.

Riemann hāpai i ka hoʻohana 'ana o ka helu o Euler, nń no a pau maoli mau> 1. Inā ka ia haʻilula ua hoʻohana 'ia no ka luna' mau, alaila, o ka hopena ua e converge no kekahi waiwai ana i ka ee iaaanu aey me ka mea maoli hapa, ua oi aku ia mamua 1. Riemann hoʻohana i ka analytic mau nō lā hoʻi o ke kaʻina hana ma ka hoʻonui i ka wehewehena o zeta (s) no nā luna 'nui, akā, "kiola" pa alima. Ka mea, ua i hiki, no ka mea, ina o = 1 zeta kuleana pili i kēia piʻina i ka infinity.

mea hiki hoohalike

Ke ninau aicieeaao: ka mea hana hoihoi a me ka nui zeta hana, i meaʻano nui i loko o ka hana o Riemann ma ka Yard kuhiakau? E like me ko oukou ike ana, i ka manawa i loaʻa i ka mea kumu hoʻohālike i hōʻike ana i ka puunaue ana o Kuhina Nui loa i waena o ka mea maoli. Riemann hiki ke huai ae i ka helu o ka pi (m) o Kuhina Nui huahelu, i mea ole i oi i ka m, ua kaheaia ma ka puunaue ana o nontrivial Aʻohe zeta kuleana pili i. A, o ka Riemann kuhiakau mea he pono ana i mea e ho'āʻo? Aiaiiuie loiloi 'ana ma o kekahi cryptographic algorithms.

Ka Riemann kuhiakau

Kekahi o na mea haʻilula keimikala mua o keia makemakika pilikia, i maopopo a hiki i kēia lā, mea: AICIeOEOI 0 zeta kuleana pili i - luna 'helu a me ka makemake loa like me ke ½. Ma nā hua'ōlelo, ka mea i hoonohonoho i pololei ka laina Re mau = ½.

Aia Ua hoi he generalized Riemann kuhiakau, i mea ka ia hoike, akā, no ka generalization o ka zeta-mana, i ka poe i kaheaia ke Dirichlet (e nānā. Photo ma lalo nei) L-hana.

Ma ka haʻilula χ (N) - he laulā pūʻulu (mod k).

Riemann ka hoakaka o ka ai-kapaia Yard kuhiakau, e like me ka ua, ua hōʻoia no ka hana mau a me ka na hāpanaʻikepili.

Like au ua kūkākūkāʻia Riemann

Note Kelemānia mathematician i mua ua kālaiʻia loa casually. Ka mea o ia i ia manawa i ka nä känaka 'epekema i ana, e hooiaio i ka theorem ma ka puunaue ana o Kuhina Nui loa, a ma keia pōʻaiapili, keia kuhiakau aʻole i nui ai. Eia naʻe, kona kūlana i kamaʻilio akula i ka nui no hoi na nīnūnē mea, alahula mau. Ia mea ke kumu o ka Riemann kuhiakau no ka manawa he nuiʻepekema ike i ka nui o unproven makemakika pilikia.

Like i ua mai la, e hooiaio i ka theorem ma ka puunaue ana o ka piha Riemann kuhiakau mea i pono, a me ka loa kekahi hoʻonohonoho hooiaio i ka maoli hapa o kekahi ole-AICIeOEOI Aʻohe o ka papa zeta mea ma waena o 0 a me 1. kēia waiwai hoʻohuʻu i ka huina o-ka m 0 a pau zeta hana eʻikea au i loko o ka kiko'ī haʻilula luna, - finite ikaika. No ka nui aiee o ka m, e hiki nā mea a pau e nalowale. Ka lala wale o ka haʻilula, a e noho kŰlń a hiki ma kiʻekiʻe loa m, m ka ia ia iho. Ke koena o ka luna 'hua'ōlelo i loko o e like me ka mea asymptotically nalo. Penei, i ke kaupaona ana, no na dala mālama i ka m. Kēia mea hiki ke manaoia i kona hoaoia'na, no ka oiaio o ke Kuhina Nui helu theorem. Ke'ī mai, kahi mea akaka i ka 'Aʻohe hualoaʻa o ke kuleana pili i Riemann zeta he kūlana kūikawā. Ua mea e hooiaio i hiki ole i kēia mau loina he hoʻonui me ka nui loa i ka anoe haʻilula.

Riemann following

Ka lono kaumaha ka make mai tuberculosis hooki ke nä känaka 'epekema lawe mai i ka Logical pau ana o ka polokalamu. Eia naʻe,ʻo ia i ka baton, mai ka W-F. ka'Aroda: Vallée Poussin a me Zhak Adamar. Kū kaʻawale o kekahi i kekahi mea, ua huli aʻe Kuhina Nui helu theorem. Hadamard a Poussin e hoʻokele i ka hooiaio i nontrivial 0 zeta kuleana pili i nā mea a pau i aia i loko o ka pilikia koa.

Mahalo i ka hana ana i kēia mau kānakaʻepekema, he hou lala o ka makemakika - mākau pähola 'o ka helu. Ma hope, ua loaa na noiʻi ka iki hou primitive hooiaio o ka theorem i hana ma Roma. Ma kekahi, ua weheia Pal Erdös a me Atle Selberg e hookupaa aku ana i kona lahui luna 'lei o ke kūpili,ʻaʻole he pono i ka hana o ka luna' Ikepili. Eia naʻe, ma keia wahi i ka manaʻo o Riemann ma kekahi mau nui theorems i ua ai, me ka kokekau o ka nui mana o ka helu kumumanaʻo. Ma pili ana me keia hou hana Erdős a me Atle Selbergʻaneʻane kekahi mea i loli.

Kekahi o ka simplest a loa nani hoike o ka pilikia, ua loaʻa i loko o ka makahiki 1980 ma Donald Newman. Ua Ua nānā 'ana ma luna o ka luawai-ike Cauchy theorem.

Hooweliweli ina Riemann ka kuhiakau o ke kumu o kēia cryptography

ʻIkepili encryption i waho me ka helehelena o ka huapalapala, a aho, ka mea, ia lakou iho i e manao like i ke kuhi mua. Ma ka manawa, aia no he okoa hou au o ka mīkini cryptography, a ua hana i loko o ka ulu ana o ka encryption algorithms.

Simple a. E. ka i mea wale maheleia i mau'ē aʻe helu o ka ia papa "Semisimple" helu m, i ke kumu o ka lehulehu kī kahua,ʻikeʻia me RSA. Ua loaʻa he ākea palapala noi. Ma kekahi, ka mea, ua hoʻohana 'ia i loko o ka hanauna o ka uila inoa. Inā mākou e'ōlelo i loko o hua'ōlelo o ka "teapot" loaʻa, ka Riemann kuhiakau hoʻike i ke ola ana o ka'ōnaehana i loko o ka puunaue ana o Kuhina Nui helu. Penei, me ka nui loa hoemiia ia'ku o cryptographic ki, ma i hilinaʻi nui o ka maluhia o online, hana ma ka e-kalepa.

Other unsolved makemakika pilikia

Piha 'atikala mea waiwai i hoʻolaʻaʻia lā i kekahi mau hua'ōlelo no nā hana o ke Ka Wā Kaukani. Mau nā:

• Like o nā papa P a me np. Ka pilikia ua ua kālaiʻia me penei: inā he maikaʻi pane i ka haawi ninau ua hōʻoia i ka polynomial manawa, a laila ka mea oiaio ia oia ia ia iho i ka pane a hiki i keia ninau hiki ke loaʻa koke?
• Hodge conjecture. Ma na mea hua'ōlelo mea hiki ke olelo ia penei: no ka mea, i kekahi mauʻano o projective algebraic lokomaikaʻi he (hakahaka) Hodge pōʻaiapuni i pu ana o ka mea i loaʻa i ka geometric hoike ana, oa algebraic pōʻaiapuni ...
• Poincaré conjecture. He ka mea wale ai ma ka manawa Ka Wā Kaukani pilikia. E like me ka mea, i kekahi ekolu-dimensional mea nona kekahi waiwai o ka 3-dimensional poepoe, pono e pololei i ka deformation ka poepoe.
• Apono o ka quantum Yang - Mills kumumanaʻo. E Pono e hooiaio ia quantum kumumanaʻo, kau aku ma kēia mau kānakaʻepekema i ka makahiki R ^4, aia no he 0-ʻaha hewa no kekahi poe noonoo ole ana o ka olelo hoopomaikai pūʻulu G.
• Ke kuhiakau o ka Birch - Swinnerton-Dyer. He pilikia kekahi mea mea pili i ka cryptography. Ua pili ana i ka elliptical curves.
• Ka pilikia o ke ola a me ka smoothness o pāʻoihana o ke Navier - Stokes nā helu kaulike.

Ano, e ike i ka Riemann kuhiakau. Ma na mea hua'ōlelo, ua ua kālaiʻia mākou a me kekahi o na'ē aʻe Pahuhopu o ka Ka Wā Kaukani. Ka mea i ka mea, e e hoʻonā 'ia paha ka mea, ua hoao aku au ia ia ka mea, i ole pāʻoihana - ia O ka mea o ka manawa. A me keia mea olelo lealea, e i ke kali lōʻihi, e like me ka makemakika i increasingly hoʻohana computational mana o ke kamepiula 'ē aʻe. Eia naʻe,ʻaʻole nā mea a pau ka malama ana i ke akamai a me ka hoʻoponopono 'epekema pilikia kuhikuhi pono kilo a me kaʻike hoʻokumu.