The Riemann kungoganizira. Kufalitsa manambala yaikulu

Mu 1900, mmodzi wa asayansi aakulu a atumwi wotsiriza, David Hilbert mndandanda ongokhala 23 mavuto sanathetsedwe wa masamu. Ntchito pa iwo wakhala akuthandiza kwambiri pa chitukuko cha munda wa nzeru za anthu. Patatha zaka 100 mu Clay masamu Institute anapereka mndandanda wa mavuto zisanu ndi ziwiri, lotchedwa zolinga Millennium. Chigamulo cha aliyense wa iwo anapatsidwa mphoto ya $ 1 miliyoni.

Vuto okha, amene anali pakati m'mabuku awiri a masamu, kwa zaka sanapereke zina asayansi, anakhala Riemann kungoganizira. Iye akadali akuyembekezera maganizo ake.

Mwachidule mbiri mudziwe

Georg Friedrich Bernhard Riemann anabadwa mu 1826 ku Hanover, mu banja lalikulu la m'busa wosauka, ndipo anakhala ndi zaka 39 zokha. Iye anazisindikizitsa mapepala 10. Komabe, pa moyo wa Riemann ankaona m'malo mwa mphunzitsi wake Johann Gauss. Pa zaka 25 achinyamata wasayansi kumbuyo nkhani yolembedwa wake "maziko a chiphunzitso cha ntchito za variable zovuta." Kenako anakonza kungoganizira wake, amene anatchuka kwambiri.

primes

Masamu anabwera pamene munthu aphunzira kuwerenga. Ndiyeno panabuka lingaliro loyamba la manambala, umene pambuyo pake anayesa m'kagulu. Zinaonetsa kuti ena mwa iwo ndi katundu wamba. Makamaka pakati pa manambala zachilengedwe m. E. Anthu amene ntchito mu mawerengedwe (manambala) kapena nambala anasankha zinthu wakhala allocated gulu la amenewa amene anagawa okha ndi chimodzi ndi iwo eni. Iwo ankatchedwa yosavuta. Umboni kaso wa Lingaliro Lovomerezeka wopandamalire ya manambala kwapatsidwa mwa Euclid wake "Zochitika". Pa nthawi, ife zikupitirirabe kufufuza kwawo. Makamaka, yaikulu angapo a kudziwika 2 ^74207281 - 1.

chilinganizo Euler a

Pamodzi ndi lingaliro la primes wamphamvu ambiri Euclid kumatanthauza ndi Lingaliro Lovomerezeka wachiwiri Zimatheka factorization. Malinga kuti aliyense inteja zabwino ndi mankhwala a kabudula mmodzi yekha primes. Mu chaka cha 1737, akulu German masamu Leonhard Euler anasonyeza loyamba Lingaliro Lovomerezeka Euclid pa malire a njira pansipa.

Njirayi imatchedwa zeta ntchito, pamene m - zonse ndi tsa ndi onse mfundo yosavuta. Kuyambira mwachindunji namtsata ndi kukondweretsa wapadera patsogolo Euclid.

Riemann zeta ntchito

chilinganizo Euler pa anayendera pafupi ndi chidwi ndithu, limene chiŵerengero pakati pa onyozeka ndi integers. Ndipotu, kudzanja lake lamanzere akuchulukitsidwa mawu wamphamvu ambiri amene amadalira yekha losavuta komanso ndi kuchuluka lamanja afanizidwanso ndi integers zonse zabwino.

Riemann anapita Euler. Pofuna kupeza kumabweretsa vuto la kufalitsa manambala, izo akufuna kufotokoza njira kwa onse variable kwenikweni ndi zovuta. Zinali iye amene anadzatchedwa monga Riemann zeta ntchito. Mu 1859 wasayansi inalemba nkhani yakuti "Pa chiwerengero cha primes kuti musalumphe mtengo anakonzeratu" omwe mwachidule maganizo ao onse.

Riemann akufuna kugwiritsa ntchito zingapo Euler, convergent onse m weniweni> 1. Ngati chilinganizo amene ankagwira ntchito m zovuta, ndiye mndandanda adzakhala converge kuti phindu la variable ndi gawo weniweni ndi wamkulu kuposa 1. Riemann ntchito kupitiriza analytic wochita ndi yowonjezera tanthauzo la zeta (s) kuti manambala zonse zovuta, koma "kuponya" unit. Sikunali kotheka, chifukwa ngati m = 1 zeta ntchito ukuwonjezeka kwa osawerengeka.

tanthauzo othandiza

funso n'lakuti: ndi zimene chidwi ndi zofunika zeta ntchito, chimene chiri chofunika mu ntchito ya Riemann pa kungoganizira null? Monga mukudziwa, pa nthawi sanapezeke chitsanzo yosavuta amene akufotokoza kufalitsidwa kwa manambala yaikulu pakati zachilengedwe. Riemann amatha kudziwa kuti chiwerengero cha PI (x) ziwerengero zazikulu, zimene siziri kuposa ×, chimaoneka ndi kufalitsa nontrivial ziro zeta ntchito. Komanso, Riemann kungoganizira ndi chikhalidwe zofunikira pofuna kutsimikizira mawunikidwe zosakhalitsa ena ma aligorivimu cryptographic.

The Riemann kungoganizira

Mmodzi wa formulations loyamba vutoli masamu, osati kutsimikiziridwa lero, ndi: zazing'ono 0 zeta ntchito - manambala zovuta ndi gawo weniweni wofanana ½. M'mawu ena, iwo anakonza pa mzere wolunjika Re m = ½.

Palinso zowombetsa mkota Riemann kungoganizira, ndilo mawu omwewo, koma generalization wa zeta-ntchito, zomwe zimatchedwa Dirichlet (onani. Photo pansipa) L-ntchito.

Mu chilinganizo χ (n) - khalidwe n'zosangalatsa kumva (yamakono k).

mawu Riemann ndi otchedwa null kungoganizira, monga wakhala kutsimikizika kwa kugwirizana ndi deta zilipo nyemba.

Monga ine kukangana Riemann

Dziwani German masamu poyambirira anakonza ndithu amangotchula. mfundo ndi yakuti pa nthawi imeneyo wasayansi ankati kutsimikizira ndi Lingaliro Lovomerezeka pa kufalitsidwa kwa manambala yaikulu, ndipo m'nkhani imeneyi, amanena alibe zotsatira kwambiri. Komabe, udindo wake poyankha nkhani zina zambiri zoopsa. N'chifukwa chake Riemann amanena kuti tsopano asayansi ambiri amadziwa zofunika mavuto unproven masamu.

Monga zanenedwa, kutsimikizira Lingaliro Lovomerezeka pa kufalitsa zonse Riemann kungoganizira Sikuti, ndipo ndithu, nawatsimikizira kutsimikizira kuti kumapangitsa aliyense sanali zazing'ono ziro wa ntchito zeta ndi pakati 0 ndi 1. katundu Izi zikutanthauza kuti Uwerenge onse 0-mamita zeta ntchito zimene zimaoneka mu dongosolo lenileni pamwamba, - amalire zonse. Pakuti mfundo yaikulu ya ×, zikhoza onse adzataika. Membala chabe wa kachitidwe, amene adzatsala zikutsatiridwa ngakhale pa × kwambiri, × mwiniyo. Otsala a mawu ovuta poyerekeza ndi izo asymptotically kutha. Motero, ndalama zolemeletsedwa amamuchititsa x. Mfundo imeneyi kutengedwa ngati chitsimikizo cha choonadi cha yaikulu Lingaliro Lovomerezeka chiwerengero. Choncho, ziro wa ntchito Riemann zeta limapezeka udindo wapadera. Ndi kutsimikizira kuti mfundo izi sangathe kwambiri kupita chilinganizo kukula.

otsatira Riemann

The imfa ku TB chinalepheretsa wasayansi kubweretsa zomveka mapeto a pulogalamuyi. Komabe, iye anatenga ndodo mwachangu, kutsogolera ku W-F. de A La Vallée Poussin ndi Zhak Adamar. Mosadalira mzake iwo anali kudzipatula yaikulu chiwerengero Lingaliro Lovomerezeka. Hadamard ndi Poussin anakwanitsa kutsimikizira kuti onse nontrivial 0 zeta ntchito ili mkati gulu yovuta.

Chifukwa cha ntchito asayansi awa, nthambi yatsopano ya masamu - mawunikidwe chiphunzitso cha manambala. Kenako, akatswiri ena analandira pang'ono wosazindikira umboni wa Lingaliro Lovomerezeka anali kugwira ntchito ku Roma. Makamaka, mnzako Erdös ndi Atle Selberg Ndatsegula ngakhale kutsimikizira unyolo ake lodabwitsa maganizo, osati kugwiritsa ntchito kusanthula zovuta. Komabe, pa nthawiyi lingaliro la Riemann ndi theorems zingapo zofunika akhala kutsimikiziridwa, kuphatikizapo chiyerekezo cha ntchito ambiri chiphunzitso chiwerengero. Mogwirizana ndi ntchito yatsopano Erdős ndi Atle Selberg chilichonse si bwanji.

Mmodzi wa losavuta ndi wokongola kwambiri umboni vuto wapezeka mu 1980 ndi Donald Newman. Izo zinali zochokera odziwika Cauchy Lingaliro Lovomerezeka.

Anaopseza ngati kungoganizira Riemann ndiwo maziko a cryptography zamakono

Data kubisa anatuluka ndi maonekedwe a chikhalidwe, kapena kani, iwo akhoza amatengedwa kuti malamulo choyamba. Pa nthawi, pali atsopano makhalidwe a digito cryptography, umene ukugwira chitukuko cha ma aligorivimu kubisa.

Zambiri ndi "Semisimple" chiwerengero m. E. Anthu amene anagawa yekha mu manambala ena awiri a m'kalasi lomwelo, ndi maziko a dongosolo anthu ofunika, lotchedwa RSA. Iwo ali ntchito lonse. Kwenikweni, ntchito mu m'badwo wa siginecha amagetsi. Ngati ife kulankhula mawu a zilipo "teapot", ndi Riemann kungoganizira ananenetsa kuti kuli dongosolo mu kufalitsa manambala yaikulu. Choncho kwambiri yafupika kulimbikira makiyi cryptographic, pa potsata chitetezo cha wotuluka Intaneti e-malonda.

Other sanathetsedwe mavuto masamu

Nkhani Complete ndi ofunika kuthera mawu ochepa kuti ntchito zina za Zakachikwi. Njirazi ndi monga:

• Kuyanjana pakathi pa makalasi P ndi NP. Vutolo anakonza motere: ngati yankho zabwino funso anapatsidwa wotsimikizika mu nthawi polenomiyo, ndiye zoona kuti iye yankho la funso limeneli lili msanga?
• Hodge kungolota. Mawu osavuta akhoza ananena motere: a mitundu ina manifolds projective algebraic (mipata) Hodge m'zinthu ndi osakaniza zinthu kuti ndi kutanthauzira zojambula, mwachitsanzo algebraic m'zinthu ...
• Poincaré kungolota. Ndi kokha kuwonedwa pa mavuto mphindi Zakachikwi. Malinga izo iliyonse chinthu atatu azithunzi omwe tikunena ndi katundu imodzi ya dera 3-azithunzi omwe tikunena, dera ayenera kukhala olondola mapindikidwe.
• Kukondweretsa kwadzidzidzi Yang - Mills chiphunzitso. Tiyenera kutsimikizira kuti chiphunzitso kwadzidzidzi, atapereka asayansi awa danga R ^4, pali chilema 0-misa kwa calibration aliyense yosavuta yaying'ono gulu G.
• The amanena za Birch - Swinnerton-Dyer. Ichi ndi vuto lina zogwirizana cryptography. Koma pali vuto zokhotakhota elliptical.
• Vuto kuli ndi smoothness njira ya Navier - Stokes maikwezhoni.

Tsopano inu mukudziwa Riemann kungoganizira. Mawu osavuta, ife anakonza ndipo ena mwa zolinga zina za Zakachikwi. chakuti zithetsedwe kapena imatsimikizirika kuti iwo alibe njira - ndi nkhani ya nthawi. Ndipo ichi ndi chodziwikiratu kuti tidikirire motalika kwambiri, ngati masamu akugwiritsa ntchito mphamvu zowerengera makompyuta. Komatu sikuti zonse umamumvera luso ndi kuthetsa mavuto sayansi makamaka kumafuna yodziŵiratu zinthu pasadakhale ndi zilandiridwenso.