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zi6a~U1_HSdFLj=q=vy)Z%&ZY*qwV1O0LTCSHIx;|iny_#I_Yc+H^cw}pqv=M|M>to zpil@DUL##%K=3c`Mya5bN)etA((KpAB+R` z2WA*2=*DjmyCgVoVnNVgH?aVLVA#zu5Vj%kdX@YY^EHj*2A>f$b|7LlxY3UtjCfdX z(4g1r*9{s6>;_K}*ZV^r2pSjU2LFISDD+Rv9H5p+xZIB)O|2!w&IO|Rdvz@Xrp z_W|MpU7L%)^+VKIzg~8Kqk%ctIc|;t=0FJjMn8l&fH%j5aDljPj>`_?fc{D2M5N9C zJ}w80;}7|AAk^UIxG)&xkNZGWmjB~=oKOht<`|q%j+;6Taj295GDixasv4P|9=-903RQQoxQ%T{a 1$ und daher durch eine Primzahl $p$ teilbar, wobei man +\begin{displaymath} + p := min\{t \in \N * | t | n \und t > 1 \} +\end{displaymath} +Wenn $p| n \und p| n-1 = p_1p_2 \cdots p_r$ folgt daraus +\begin{displaymath} + p|1 = N-1(N-1) \text{Wiederspruch!} +\end{displaymath} +Also ist $| \P | = \infty$, \hfill$\blacksquare$ +\subsection*{Anmerkung 1.21} +\begin{eqnarray*} +\sum_{p\in\P} \frac 1 p && \text{divergent (Euler)}\\ +\sum_{k=1}^{\infty} &=& \frac{\pi^2}{6} +\end{eqnarray*} +\subsection*{Anmerkung 1.22} +\begin{displaymath} + \pi(x) = \{ p \in \P | p \leq x\}, x\in \R^+ +\end{displaymath} +Primzahldichte in der Nähe von $x \approx \frac 1 {ln(x)}$\\ +in der Gegend von $10^{100}$ : jede $\approx 230.$ Zahl ist eine Primzahl + +\subsection*{Riemansche Vermutung} +\begin{displaymath} + \zeta(s)= \sum_{n=1}^{\infty}\frac 1{n^s} \hfill (re(s) >1) +\end{displaymath} +Analytisch fortzetzen: +\begin{eqnarray*} + \zeta(s) & = & 1 + \frac 1{2^s} + \frac 1{3^s} + \frac 1{4^s} + \frac 1{5^s} + \cdots\\ +\frac 2 {2^s}\zeta(s) & = & \frac 2{2^s} + \frac 2{4^s} + \frac 2{6^s} + \cdots\\ +(1-2^{1-s})\zeta(s) & = & 1 - \frac 1{2^s} + \frac 1{3^s} - \frac 1{4^s} + \frac 1{5^s} - \cdots = \eta(s)\\ +\zeta(s) & = & \frac{\eta(s)}{(1-2^{1-s})} +\end{eqnarray*} + +Riemann-Siegel-Formel? + + + + +\end{document} diff --git a/ue1.pdf b/ue1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..84ddd906d1af8fc42d7d979368420a389cb64f30 GIT binary patch literal 73100 zcmbrlWl&vB(>97jAh;&j#x*$XO@QF;PH?y2?(Xgq+=IKjCOAQZI|O&Pvq|pzeV+53 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Aufgabe} + +\begin{eqnarray*} +&&\begin{array}{ccccccc} + r_{i-2} & r_{i-1}& q_i & x_{i-2} & x_{i-1} & y_{i-2} & y_{i-1}\\ + 312 & 269 & 1 & 1 & 0 & 0 & 1\\ + 269 & 43 & 6 & 0 & 1 & 1 & -1\\ + 43 & 11 & 3 & 1 & -6 & -1 & 7\\ + 11 & 10 & 1 & -6 & 19 & 7 & - 22\\ + 10 & 1 & & 19 & -25 & -22 & 29\\ +\end{array}\\ +\text{ggT}(312,269) & = & 1\\ +1 & = & -25*312+29*269\\ +5 & = & -125*312+145*269\\ +x & = & 5\cdot\binom{-25}{29}+\cdot +\end{eqnarray*} + +\end{document} -- 2.47.3