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Le sue propriet, ogni tanto, si svelano all uomo matematico con pigrizia e avarizia ( per consentire a qualcuno di conseguire il premio Wolf o la medaglia Fields, sorta di Nobel della matematica ).B %  33___PPT10i.\ +D=' = @B +" ''v(  =   x9%0e0e?Rectangle 2 t 0 q Funzione zeta di Riemann$  $    x:%0e0e?Rectangle 6/U  0 Definiamo la funzione Con n N ed m il numero dei primi minori di n. Esempio: Perch due sono i numeri primi minori di 5 e questi sono 2 e 3.(O P] P    TA ??Object 7 \   TA ??Object 9n  tB  L?Line 10 tB  L?Line 11vgSvnB   F?Line 12InB   F?Line 13I==nB   F?Line 15InB   F?Line 16I nB  @ F?Line 18I] ] nB  F?Line 19I  nB  F?Line 20 w nB  F?Line 21 w nB  F?Line 22V wV nB  F?Line 25 w nB  F?Line 26 w   N?Text Box 27v] W1     N g?Text Box 28U< W0     Hi?Text Box 29vy] W2     N@hC?Text Box 30vj. ] W3     NV?Text Box 31v ] W4     N?Text Box 32v ] W5     N Q?Text Box 33v | ] W6     N ?Text Box 349   W1     N?Text Box 35 j  W2     NZ?Text Box 36   W3     N=%?Text Box 37   W4     N>%?Text Box 38c J  W5      N:?Text Box 39 J Wx    ! N :?Text Box 40 - Wx    " N@:?Text Box 41  Wx    # N`:?Text Box 429   Wx    $ N:?Text Box 439 T  Wx    % N:?Text Box 44 M  Wx    & N:?Text Box 45   Wx    ' N:?Text Box 46 t  Wx     \A ? ?Object 47c6  33___PPT10i.\.+D=' = @B +"      (      x1%0e0e?Rectangle 4T  0 OGauss studi la funzione con x R nel tentativo di estrarre dalla discretezza di una funzione continua. La funzione con x R, invece di n N, stata chiamata funzione zeta ed indicata col simbolo z(x). Legendre nel 1798 congettur che, per x sufficientemente grande, dove A e B sono costanti da determinare. Successivamente, nel 1808, Legendre afferm che possibile trovare, con soddisfacente approssimazione, che fra 1 e un certo numero limite x, ci sono y numeri primi e precisamente PP O P 0  xA ? ?Object 7 (  0 0  xA ? ?Object 9m z(  0 0  zA ? ?Object 11z:y(  0  \A ? ?Object 13/J$   VA ??Object 20, ?   VA  ??Object 21)  I   0  zA  ? ?Object 23]j(  0   \A  ? ?Object 25] }      VA  ??Object 26  $     VA  ??Object 27    33___PPT10i.7]@+D=' = @B +" c  jb  J(      x`6%0e0e?Rectangle 4  0 2B.Riemann (1826-1866) si spinge oltre e pone il problema per s complesso. Cio la funzione z(s) con s=a+bi numero complesso. Questa funzione stata chiamata funzione zeta di Riemann e indicata col simbolo Riemann afferm (di qui la CONGETTURA di RIEMANN tuttora non dimostrata) che l equazione con s=a+bi, tale che a=1/2 per ogni b. Cio gli zeri complessi di hanno la parte reale sempre uguale a 1/2. In altre parole, gli zeri della funzione zeta si trovano sulla retta di equazione x=1/2 parallela all asse delle y.h  3    0 lA ? ?Object 5` & (  0  0  xA ? ?Object 7z m #(  0  0  zA ? ?Object 13n 9_ (  0 33___PPT10i.;]+D=' = @B +" / 0 o(     H1%?Rectangle 4 hL OPERA DI BERNHARD RIEMANN Una fase di notevole importanza nello studio della funzione z associata agli studi di Riemann, il quale propose (1859) di definire tale funzione per x T C e si occup del prolungamento analitico di z all intero piano complesso. Gli zeri della funzione z cos prolungata ( z ammette un polo per z = 1 ) sono:d 9  ", O  J5%?Rettangolo 6bm  x = -2, x = -4, x = -6, ... detti zeri banali di z; alcuni numeri complessi (non reali) x, con parte reale 0<=Re(x)<=1 Riemann suppose che tutti gli zeri non banali di z siano caratterizzati dalla propriet di avere parte reale Re(x)=. La congettura indicata da Riemann non ancora stata provata n smentita; nel 1914, G.H. Hardy giunse a dimostrare che z ha infiniti zeri non banali per i quali risulta verificata la supposizione Riemanniana.t    H  .B   3380___PPT10.l]@#?g" @$(  $ $ H6%?Rectangle 4\>  +Essendo la congettura di Riemann collegata alla serie dei numeri primi dalla formula di Eulero, e alle formule per il calcolo del numero di numeri primi, alcuni pensano che un'eventuale dimostrazione di questa congettura potrebbe aprire la strada alla scoperta di nuovi pi efficienti metodi per fattorizzare un numero nei suoi fattori primi, e quindi minare le fondamenta del cifrario RSA  #  3380___PPT10.X]В"# {Pc(  x  s <A ??Object 50    TA ??Object 7    X`0%?"CasellaDiTesto 5 3Una rappresentazione della funzione zeta di Riemann4 4 4  3380___PPT10.Y]p:"  kc`K(    TA ??Object 5+a     TA ??Object 6p    TA ??Object 9   VA ??Object 105Z    VA ??Object 11     RC?"CasellaDiTesto 9;:^ ;Alcuni valori della funzione zeta < < <  3380___PPT10.j]ì" p((  ( ( T@C?Rectangle 4MW4 4Louis de Branges de Bourcia della Purdue University 5 5 5  ( T@:?Rectangle 5 -ha affermato di aver dimostrato l'ipotesi di . . .  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D@;q rsܘ}n%C@MMD8hx>^6yXkYq9Z'ɦxCt+B %97|_!F#Oh+'0 X`x    Il numero esisteva ancor prima che luomo comparisse sulla terra. Le sue propriet, ogni tanto, si svelano alluomo matematico con pigrizia e avarizia ( per consentire a qualcuno di conseguire il premio Wolf o ila medaglia Fields, sorta di Nobel della matematica ).studentNicola39Microsoft Office PowerPoint@@ V*@P4&\@sG\՜.+,D՜.+,X    $  Presentazione su schermo (4:3) salvemini<  ArialCalibriStruttura predefinitaMicrosoft Equation 3.0Immagine di Microsoft WordIl numero esisteva ancor prima che luomo comparisse sulla terra. Le sue propriet, ogni tanto, si svelano alluomo matematico con pigrizia e avarizia ( per consentire a qualcuno di conseguire il premio Wolf o la medaglia Fields, sorta di Nobel della matematica ). Funzione zeta di RiemannPGauss studi la funzione con x R nel tentativo di estrarre dalla discretezza di una funzione continua. La funzione con x R, invece di n N, stata chiamata funzione zeta ed indicata col simbolo z(x). Legendre nel 1798 congettur che, per x sufficientemente grande, dove A e B sono costanti da determinare. Successivamente, nel 1808, Legendre afferm che possibile trovare, con soddisfacente approssimazione, che fra 1 e un certo numero limite x, ci sono y numeri primi e precisamente B.Riemann (1826-1866) si spinge oltre e pone il problema per s complesso. Cio la funzione z(s) con s=a+bi numero complesso. Questa funzione stata chiamata funzione zeta di Riemann e indicata col simbolo Riemann afferm (di qui la CONGETTURA di RIEMANN tuttora non dimostrata) che lequazione con s=a+bi, tale che a=1/2 per ogni b. Cio gli zeri complessi di hanno la parte reale sempre uguale a 1/2. In altre parole, gli zeri della funzione zeta si trovano sulla retta di equazione x=1/2 parallela allasse delle y.Diapositiva 5Diapositiva 6Diapositiva 7Diapositiva 8Diapositiva 9-Grafico tridimensionale della funzione zeta Caratteri utilizzatiTemaServer OLE incorporatiTitoli diapositive  8@ _PID_HLINKSAGhttp://www.liceofoscarini.it/studenti/crittografia/critto/rsa/rsa.html7http://www.math.purdue.edu/ftp_pub/branges/apology.pdfGhttp://www.liceofoscarini.it/studenti/crittografia/critto/rsa/rsa.html7http://www.math.purdue.edu/ftp_pub/branges/apology.pdf_FNicolaNicola  !"#$%&'()*+,-./0123456789:;<=?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Root EntrydO)Pictures{Current UserSummaryInformation(PowerPoint Document(>FDocumentSummaryInformation8