The Riemann pfungwa. Distribution inonyanya nhamba

Muna 1900, mumwe mukuru masayendisiti remakore rapfuura, David Hilbert akaita pasi rine 23 matambudziko unsolved wemasvomhu. Basa iri kwavari rwave chaizvo kwakabatsira kukura munda uyu ruzivo kwevanhu. Pashure pemakore 100 muna Clay kwemasvomhu Institute akauya pasi matambudziko manomwe, inonzi Millennium zvinangwa. Nokuda kwezvaizosarudzwa neimwe akapiwa mubayiro $ 1 miriyoni.

The dambudziko chete, waiva pakati mazita maviri Puzzles, kwemazana emakore haana kupa zororo kuna masayendisiti, akava Riemann pfungwa. Ari vakamirira sarudzo yake.

Brief oupenyu mashoko

Georg Friedrich Bernhard Riemann akaberekwa muna 1826 muna Hanover, mune imwe mhuri huru imwe mufundisi murombo, uye akararama makore 39 chete okuberekwa. Akakwanisa kubudisa 10 mapepa. Zvisinei, munguva upenyu Riemann iye vanoonekwa akatsiva mudzidzisi wake Johann Gauss. At makore 25 musayendisiti muduku akadzivirira chinyorwa chake "nheyo dzidziso mashandiro anoita kunzwisisa shanduka." Gare gare iye akagadzira pfungwa yake, rwakazokura nomukurumbira.

of times

Masvomhu akauya apo murume vakadzidza kuverenga. Ipapo pfungwa nhamba, iyo gare gare akaedza patsanura wokutanga. Zvave zvichinzi kuti vamwe vavo vave nevakawanda ehupfumi. Zvikurukuru pakati dzinongoitika nhamba m. E. izvo zvaishandiswa dzemaitirwe (vakaverengwa) kana akasarudzwa nhamba zvinhu kwave dzinounzwa boka vakadaro ayo akakamurwa chete nomunhu uye pachavo. Vakadaidzwa nyore. An yakashongedzwa uchapupu theorem no kusingaperi akagadzirwa nhamba chakapiwa Euclid mu "Elements" ake. Panguva iyoyo, tiri kuramba kutsvaka kwavo. Kunyanya, kupfuura nhamba yaizivikanwa ² 74207281 - 1.

Euler kuti fomura

Pamwe pfungwa of times zvikuru zvakawanda Euclid chinorondedzerwa uye theorem no wechipiri chete zvinoita factorization. Maererano zvacho zvakanaka integer ndiye chigadzirwa mumwe chete iine of times. Muna 1737, mukuru German yemasvomhu Leonhard Euler akaratidza yokutanga Euclid kuti theorem no pamusoro zvisingaperi kune nzira pasi apa.

Inonzi Zeta basa, apo s - kugara uye peji zvose nyore tsika. Kubva kuzoti zvakananga uye kufarirwa yokusiyana pakuwedzera Euclid.

Riemann Zeta basa

Euler kuti fomura pamusoro ukanyatsozvitarisa rakanyatsojeka kunoshamisa, sezvo inopiwa nhamba pakati mano uye integers. Pashure pezvose, murutivi rwahwo vowanda mashoko zvikuru zvakawanda kuti kuvimba chete nyore, uye zvisingatori nguva yakawandisa Rinobatanidzwa zvose zvakanaka integers.

Riemann akaenda Euler. Kuti awane kiyi dambudziko riparadzirwe nhamba, hazvina ndaizvipira rinotsanangura nzira vose chaiye uye kunzwisisa shanduka. Zvakanga iye akazova seshanduro Riemann Zeta ishande. Muna 1859 musayendisiti yakabudisa nyaya yaiva nomusoro waiti "On uwandu of times kuti haapfuuri akafanorongerwa ukoshi", iro muchidimbu pfungwa dzavo dzose.

Riemann akafunga kushandisa wandei Euler, convergent vose chaidzo S> 1. Kana chete payakavakirwa rinoshandiswa kuti kunzwisisa s, ipapo dzinotevedzana ichapindura wekuita upi kukosha shanduka chete chaiye chikamu mukuru 1. Riemann akashandisa analytic kuenderera nzira kuburikidza kuwedzera tsanangudzo Zeta (s) nokuti kunzwisisa nhamba zvose, asi "kukanda" chimwe. Zvakanga zvisingaiti, nekuti kana S = 1 Zeta basa inowedzerawo kuti kusaverengeka.

hunoshanda pfungwa

The mubvunzo unomuka: chii zvinonakidza uye zvinokosha Zeta basa, izvo rwakakosha basa Riemann pamusoro null pfungwa? Sezvaunoziva, panguva haana kuwana muenzaniso nyore kuti rinotsanangura kuparadzira wehurumende nhamba pakati zvepanyama. Riemann akakwanisa kuziva kuti uwandu Pi (x) inonyanya nhamba dzisiri nokure X, inoratidzwa kuparadzira nontrivial razero Zeta chaitika. Zvakare, Riemann pfungwa chinhu chinodiwa chimiro kuti aratidze kwenguva Mutengo mamwe algorithms cryptographic.

The Riemann pfungwa

Mumwe Formulations uyu dambudziko kwemasvomhu pakutanga, kwete rikaratidzwa nhasi, ndiyo: sezvisingakoshi 0 Zeta basa - dzakaoma nhamba pamwe chaiko chikamu yakaenzana ½. Nemamwe mashoko, ivo vakaronga pamusoro yakarurama mutsetse Re S = ½.

Panewo generalized Riemann pfungwa, inova chete mashoko, asi nokuda zvavo pamusoro Zeta-mashandiro, vanonzi Dirichlet (ona. Photo pazasi) L-mabasa.

Muna yemaitiro χ (n) - iri kusanganiswa hunhu (Mod k).

Riemann okuti ndiwo anonzi null pfungwa, sezvo yave zvinosimbiswa kusachinja-chinja vaine aivapo mharidzo Data.

Sezvo ini nharo Riemann

Note yemasvomhu German pakutanga akagadzira zvikuru zvachero. Chokwadi ndechokuti panguva iyoyo musayendisiti achizoita kuratidza munhu theorem no pamusoro kuparadzirwa wehurumende nhamba, uye ichi chechinyorwa, pfungwa iyi asina zvikuru kushanda. Zvisinei, basa rayo paakataura mamwe nyaya dzakawanda zvikuru. Ndokusaka Riemann pfungwa zvino masayendisiti akawanda vanoziva inokosha unproven matambudziko akarongeka.

Sezvo yave akati, kuratidza kuti theorem no musi pakugoverwa zvizere Riemann pfungwa haisi zvakakodzera, uye zvikuru zvine musoro kuratidza kuti zvechokwadi chikamu chero non-duku razero ari Zeta basa iri pakati 0 uye 1. pfuma Izvi zvinoreva kuti mubatanidzwa zvose 0-M Zeta basa kuti anowanika mune chaiwo payakavakirwa kumusoro, - finite kugara. Nokuti chikuru tsika X, unogona zvose ugorasika. The chete nhengo yemaitiro, izvo vacharamba kuchinja kunyange yakakwirira chaizvo X, X pachake. Vamwe kunzwisisa mazwi kuchienzaniswa naro asymptotically kunyangarika. Saka weighted Verengai ruchigona x. Izvi zvinogona kunzi sechiratidzo chokwadi inonyanya nhamba theorem no. Nokudaro, zeros of Riemann Zeta basa anooneka basa rinokosha. Zviri kuratidza kuti tsika idzi havagoni kubatsira yekudyidzana kuti kuwedzera fomura.

vateveri Riemann

Nezvorufu kubva tibhii chaitadzisa musayendisiti kuunza musoro kumugumo chirongwa. Zvisinei, akatora Baton kubva W-F. of the Vallée Poussin uye Zhak Adamar. Pasina mumwe vaenda chikuru nhamba theorem no. Hadamard uye Poussin akakwanisa kuratidza kuti zvose nontrivial 0 Zeta basa dziri mukati dzinonetsa bhendi.

Nemhaka basa masayendisiti izvi, bazi idzva wemasvomhu - Analytical dzidziso nhamba. Gare gare, vamwe vaongorori vakagamuchira zvishoma chinyakare uchapupu theorem no yaiparidza muRoma. Zvikurukuru, DEVI Erdös uye Atle Selberg ndashama kunyange achisimbisa wayo zvikuru kunzwisisa pachiremera pfungwa, kwete zvinoda kushandisa zvakaoma kuongorora. Zvisinei, panguva iyi pfungwa Riemann kubudikidza theorems zvinokosha akawanda kunge nekusimba, kusanganisira rakada zvakawanda mashandiro anoita nhamba dzidziso. Maererano basa idzva iri Erdős uye Atle Selberg chinenge chinhu asina kukanganiswa.

Rimwe nyore uye yakaisvonaka uchapupu dambudziko awanikwa muna 1980 na Donald Newman. Zvakange kwaibva aizivikanwa Cauchy theorem no.

Pangozi kana Riemann kuti ndeyokuti hwaro cryptography ano

Data encryption yakabuda vane chimiro vatambi, kana pane, ivo pachavo chingarangarirwa sechinoitika wokutanga bumbiro iri. Panguva iyoyo, pane chitsva kuitika yose digitaalinen cryptography, riri mubasa kukura encryption algorithms.

Simple uye "Semisimple" nhamba m. E. Avo ayo chete rakakamurwa dzimwe nhamba mbiri mukirasi chete, ndivo hwaro paruzhinji inokosha gadziriro, aizivikanwa RSA. It ane yakafarikana kushanda. Zvikurukuru, rinoshandiswa parudzi wemagetsi siginicha. Kana isu kutaura nemashoko ari iripo "greene", iro Riemann pfungwa inotaura kuvapo wemuTesitamende kuparadzirwa inonyanya nhamba. Saka, yekudyidzana kwakaderedza nemishonga ine cryptographic makiyi, iro zvinoenderana kuchengeteka paIndaneti kwema mu e-zvokutengeserana.

Other unsolved kwemasvomhu matambudziko

Nyaya Complete ndewe vagotevera mazwi mashoma mamwe mabasa ari chemakore. Idzi dzinosanganisira:

• Kuenzana nemakirasi P uye NP. Dambudziko zvaitwa nemutoo sezvinotevera: kana munhu mhinduro akanaka kune mubvunzo yakapiwa zvinosimbiswa mu polynomial nguva, zvino ichokwadi kuti iye pachake mhinduro yomubvunzo uyu inogona kuwanika nokukurumidza?
• Hodge fungidziro. Zviri nyore zvinogona kudonongodzwa sezvinotevera: vamwe mhando projective algebraic manifolds (dzezvimwe) Hodge Zvinonzi vari mubatanidzwa zvinhu kuti vane geometric dudziro, kureva algebraic zvinogara ...
• Poincaré fungidziro. Ndiyo chete nekusimba panguva chemakore matambudziko. Maererano zvacho-dimensional matatu chinhu rine zvakananga ehupfumi of 3-dimensional bhora, nokure anofanira yakarurama kuti deformation.
• Nokubvumira quantum Yang - Mills dzidziso. Tinofanira kuratidza kuti quantum dzidziso, akaisa mberi nemasayendisiti izvi pazvakaringana R ^4, pane 0 guru kuremara chipi nyore calibration ane tsindirana boka G.
• Pfungwa yacho Birch - Swinnerton-Dyer. Ichi chimwe dambudziko iri kuhupenyu cryptography. It chokuita elliptical makakombama.
• Dambudziko ariko uye kumeso zvinogadzirisa of Navier - Stokes equations.

Zvino imi munoziva Riemann pfungwa. Zviri nyore, tine akagadzira uye vamwe zvinangwa chemakore. Chokwadi kuti vachanzwikwa kugadziriswa kana ichiidzwa kuti havana mhinduro - zvinoita nguva. Uye ichi angangotadza kumirira nguva refu, sezvo samhu vari kuramba vachishandisa computational simba makombiyuta. Zvisinei, kwete zvose zviri pasi unyanzvi uye kugadzirisa matambudziko kwesayenzi kunonyanya zvinoda kunzwisisa zvinhu uye.