From f1b30ddde9b8bcab19f6cdc3dd3cd5dc31266162 Mon Sep 17 00:00:00 2001 From: Stefan Kebekus Date: Wed, 17 Dec 2025 13:10:50 +0100 Subject: [PATCH] =?UTF-8?q?Working=E2=80=A6?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 13-applResiduum.tex | 12 ++++++------ 16-Zahlentheorie.tex | 11 ++++++++++- 16-taubersatz.png | Bin 0 -> 10481 bytes 3 files changed, 16 insertions(+), 7 deletions(-) create mode 100644 16-taubersatz.png diff --git a/13-applResiduum.tex b/13-applResiduum.tex index 1108958..ccbbc6f 100644 --- a/13-applResiduum.tex +++ b/13-applResiduum.tex @@ -234,13 +234,13 @@ skizziere das Vorgehen am Beispiel rationaler Funktionen. nach $-r$ zurück. \end{itemize} \begin{figure} - \begin{center} - \includegraphics[width=8cm]{13-integration.png} - \end{center} + \begin{center} + \includegraphics[width=8cm]{13-integration.png} + \end{center} - \caption{Integrationsweg} - \label{fig:13-1-1} -\end{figure} + \caption{Integrationsweg} + \label{fig:13-1-1} + \end{figure} Dann hängt das Integral über $γ_r$ nicht von $r$ ab, und es gilt nach dem Residuensatz diff --git a/16-Zahlentheorie.tex b/16-Zahlentheorie.tex index 69a0a68..04e4d4f 100644 --- a/16-Zahlentheorie.tex +++ b/16-Zahlentheorie.tex @@ -586,7 +586,16 @@ besondere Kürze und damit relativ hohe Zugänglichkeit bekannt. \[ U := \{ z ∈ ℂ \::\: |z| \le R \text{ und } \mathfrak{Re}(z) ≥ -δ(R) \} \] - holomorph ist. Es gilt: + holomorph ist. Wir zerlegen den Rand von $U$, die in Abbildung~\ref{fig:16-1-1} gezeigt. + \begin{figure} + \begin{center} + \includegraphics[width=8cm]{16-taubersatz} + \end{center} + + \caption{Rand der Menge $U$} + \label{fig:16-1-1} + \end{figure} + Es gilt: \[ ∂ U = \underbrace{\{ z ∈ ∂ U \::\: \mathfrak{Re}(z) > 0 \}}_{:= C_+} ∪ \underbrace{\{ z ∈ ∂ U \::\: \mathfrak{Re}(z) < 0 \}}_{:= C_-} diff --git a/16-taubersatz.png b/16-taubersatz.png new file mode 100644 index 0000000000000000000000000000000000000000..3fc5ca0fe7fa2c5bb6dad01a5e82a95bf7c12a28 GIT binary patch literal 10481 zcmb7qbySsKx9%pCR6^+vL1~Z@kS?i>2uMhmfHcyuQAsJ0ZUF@mkPxIxT0lffNok}@ zI?mj`@4NSobH4k}dB=nWhmeF2M@%y# z0!A1S_vB@?y~frjeIIFCo#Sk6rVzC9^)@50y3}jJ0##n8enGC88^2VK9p)0c&!u2U z;nbv)Bsj_Cat-U@C6NU8hL4`DJFgAi-t<N*N3dU6NS36WLire{VVq}#C&2o8D#LUS8-@)8Gu&<4@p%wqiK0D_DN zfq3ur|K9j#pg-tMQ4!%S1j6~#Y;jT1D@^B1-9oZ(`7R7Gn#&^lSXXaTN2w-q)%g6i zQ&3Q_wq`S+$93CAq{n7v2Am$c>^`xSlf%NqfK@%8{3>rB8#Blqct5-{*BQe?48l3f z>*|g~(TJp{r$2xGJZ!l)<#rb~$Vyx0y=yHZQdM7Hf3&-_>s7zI)Sr}?$V?93(W{@B zn23ywOiWA+3kx%D@Y(i~$kwa|37B8T#PoM}%gDn{OSKCM3ikK+G zr~MBW)0_fM)~nJ)oD~0gOWCJEl7&UCaJcbc%J<{PkBc}jUc4Zp6PsUOpM0m9Bz3+W zql_npg~5#282IDP7FU4Gl8j?VHeR?85yd2MK4fMJ??@ z<0EE5nDT(?|Bqh(<1GGT;D38K=+pXdlb{DmH8C?ZLazso_u|yFm^Kew&G>}r38G`!gF1euri@w$M|(#{Ys!w+RxBlP;zbZV#EdfNA2axG6aQb+!6n9U z4$98tuPm3~CyDVgpA9F*0|VpAYE1OBk<9(tc!01U?;P@Hd5$67{-S+un9kCDn62sh z>^Nyk*ITA+0&^J0Vy8^){y@OF9>a=ot|hAusdQzNo1AMxIy!D_Ox6{C_&|IMlqg1M z&+sGh^}RFE&DhjbG3(ysw{PFx&s9tSL(qm<+zE9Z<=d7&jGtXrilJB6&^TW;x$s%+ zrSkPX$q@Ja_dA%kNMg&%ic5NWdRUlWw3ONnf7qVuM5c?z_AfQ^#coclBL7cLN*MOQK_9V#33jmM#S5n=vv{R&!Ph{pIJ{Je8cMYptseU`$`+MLRY zioKepOqLwgBp$qAS+G!S!k}>KK$|_f2KXv{5>ciucelTEHdE>?n5P9^mp#4Y@ zm4IcKHitqzS}%!uN6r@gEFI0LPs}C44c|@q>Q6T6RNnnKwK6ly*2s5rbxpl(qw(Ou z;PXoaued=DF0!nC@WZ3?lg&Pp%)7pcX30N){yaTBRZkPHsjX#ZX6yy0xfx;>_Ws?w z_S1z%|C8(Z3hwTEKg%rm6|i8xdcuiTLexlO zzjYnIp`pRh(6Gv3oScdZK4$rD)ZF#m_ww~^I$BJFnQtQ}5yTo*m=fy&PNH8q^<`u) z<#Mx3u@}8%|6@<(&z)l6Ei!FZaic9s%fGg)Q+GC;A;A0M{A}>Yk0(!_xQk8p@HU-p z)NTGi@p!A>yLS(XG->ep`)4qph*p#_sV7z#RJvTSZrIGJYH3GQ$`hyVc>A8=w~9xW z+N1Y|`sT0S>r08uZka#4)pKpzO^N?2*T}}Z&}lj5*uC}fq_Co*qC_tJoo3IAtxzfV z&8fQr0_AVsyg{KRc!?p@B16l9O(>PdwBn}4bj1S0l;>MsO6YZVWo4SK_e}W;AfG%g z9zR<6JZkJ4H5MQ#EGSs+AnrOzyxirL4=<^eQ~_MUI&qVcPb8nwra8;7>c1H0luC5zb=x!NX!2WRHel= z_^*Jkg)g^-U+avf1M3>A_jWTkXD$!Y;OF=Tu}T+uKV^H>clm+w<{va3~<X-fT71iVsst1;^ zOZF)`I@-MKXG=@V$jC@{_dQ19t&JB%mq43MUx&WFcOoV!yZl2(;8;b#uIs0KhqZv< zZ8jki)uLER3{H2~vcU<)*WH%+8W}$x3yL^SP>MSLZYb2F3Nh2)e@6G@(63SRX1&|e zx2%g(8~T_|zDRlI*lx>%OqK+dK9f|nywucG-=-_}f~g@Pmv`s5dQvZJKl%pC&aAB! zY2KWeoNTDCuk~18SzF^G#_g3tY{g=lA4dxdlwSSwas^+$sTmL~{fu=Fh zK|<4Z!zEjDd1i*+`L{GAUC6{1ozak0-PUX2sjKU;6u`m3sd>Z`t4vErcM0>^QI^A5 z3FusxBjM@Or=ZcOs3`b@3_@l?LS1qLEeC=>++#WU&V zrQK~8EDn0HUo8d+9h@dgm{fR1VeHmNTBKs6NLkD~{C{;4jnDQa5kjWMyR)71iS+ubRszXud!W#X~x|REj%tnMmoGQq($E zMrmh%<2FHVe6CUqo0F)Z=fgwtq9{aetX;jNig?rq+HrEeL4tZb~UjjNqy3Wp^xPIu)(2)!2)9`+i=U}2Sl-DFf$ zRGd&W>j^rcpUtZ2fV!HRJDi-WLj@03M@x`uYJM}p6yRQ$iRho$+eh4?m2Q_~pZ)#2 zxuGdujg3akeffK~+_2qKMa7Pp*3cv#BRdO=+fRO$@>_Hq9v#h0aG^6sW>i#P7zvAF zB;|d5eeb>Hfd=1$jq$1yKrV9-vIQR#Ym{P`(Fl|(b1@%MJ$yLY9mmcf;pNK<$2--7&1or+X=rE&URWQmD%9p+eF1nm+S$#`u+;Qf&GN-|3@VaA>Kww7 zSjN?E5IXRILX-cA2MTo&OhEB1{m$<3-&M9aynp`10@+UTY;W)ijqu~jvE=0Bwzf8t zX(B4LU}o^%0hmXB%5C<$cl~GE!fn2#^HWEKT_Pir))VZ$0y_eLJY8l1u;#9Hf96>? 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