This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) %&-line parsing enabled. entering extended mode (./talk.tex LaTeX2e <2005/12/01> Babel and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, croatian, bulgarian, russian, ukrainian, czech, slovak, danish, dut ch, finnish, finnish, french, basque, french, german, ngerman, german, ngerman, greek, monogreek, ancientgreek, ibycus, hungarian, hungarian, italian, italian , latin, latin, mongolian, mongolian, norsk, norsk, coptic, esperanto, estonian , icelandic, indonesian, interlingua, romanian, serbian, slovenian, turkish, up persorbian, welsh, polish, polish, portuguese, portuguese, spanish, catalan, ga lician, spanish, catalan, galician, swedish, swedish, loaded. 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(./talk.aux) (/usr/share/texmf-texlive/tex/latex/cyrillic/ot2cmr.fd) (/usr/share/texmf-texlive/tex/latex/psnfss/ot1phv.fd) (/usr/share/texmf-texlive/tex/latex/hyperref/nameref.sty (/usr/share/texmf-texlive/tex/latex/oberdiek/refcount.sty)) (./talk.out) (./talk.out) (./talk.nav) [1{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map} ] [2] (/usr/share/texmf-texlive/tex/latex/amsfonts/umsa.fd) (/usr/share/texmf-texlive/tex/latex/amsfonts/umsb.fd) (/usr/share/texmf-texlive/tex/latex/jknapltx/ursfs.fd) [3 <./graphics/mikio_sato.png (PNG copy)> <./g raphics/tate_on_slide.png (PNG copy)>] [4] (./talk.vrb ) [5 <./graphics/hist-1000.png>] [6 <./graphics/hist-10000.png>] [7 <./graphics/hist-100000.png>] [8 <./graphics/hist-1000000.png>] [9] [10] [11] (./talk.vrb (/usr/share/texmf-texlive/tex/latex/psnfss/ot1pcr.fd) Overfull \hbox (14.63974pt too wide) in paragraph at lines 7--7 []\OT1/pcr/m/n/10.95 sage: e37a = SatoTate(EllipticCurve('37a'), 10^6)[] Overfull \hbox (14.63974pt too wide) in paragraph at lines 7--7 []\OT1/pcr/m/n/10.95 sage: show(e37a.plot_Delta(10^3, plot_points=400,[] Overfull \hbox (27.77972pt too wide) in paragraph at lines 7--7 [] \OT1/pcr/m/n/10.95 max_points=100), ymax=0.1, ymin=0, figsize=[10,3])[] Overfull \hbox (61.45703pt too wide) in paragraph at lines 10--11 [][] ) [12 <./graphics/37a-plot_Delta-1000.png>] (./talk.vrb Overfull \hbox (14.63974pt too wide) in paragraph at lines 7--7 []\OT1/pcr/m/n/10.95 sage: e37a = SatoTate(EllipticCurve('37a'), 10^6)[] Overfull \hbox (14.63974pt too wide) in paragraph at lines 7--7 []\OT1/pcr/m/n/10.95 sage: show(e37a.plot_Delta(10^4, plot_points=200,[] Overfull \hbox (27.77972pt too wide) in paragraph at lines 7--7 [] \OT1/pcr/m/n/10.95 max_points=100), ymax=0.1, ymin=0, figsize=[10,3])[] Overfull \hbox (61.45703pt too wide) in paragraph at lines 10--11 [][] ) [13 <./graphics/37a-plot_Delta-10000.png>] (./talk.vrb Overfull \hbox (14.63974pt too wide) in paragraph at lines 7--7 []\OT1/pcr/m/n/10.95 sage: e37a = SatoTate(EllipticCurve('37a'), 10^6)[] Overfull \hbox (14.63974pt too wide) in paragraph at lines 7--7 []\OT1/pcr/m/n/10.95 sage: show(e37a.plot_Delta(10^5, plot_points=200,[] Overfull \hbox (27.77972pt too wide) in paragraph at lines 7--7 [] \OT1/pcr/m/n/10.95 max_points=100), ymax=0.1, ymin=0, figsize=[10,3])[] Overfull \hbox (61.45703pt too wide) in paragraph at lines 10--11 [][] ) [14 <./graphics/37a-plot_Delta-100000.png>] (./talk.vrb Overfull \hbox (14.63974pt too wide) in paragraph at lines 7--7 []\OT1/pcr/m/n/10.95 sage: e37a = SatoTate(EllipticCurve('37a'), 10^6)[] Overfull \hbox (14.63974pt too wide) in paragraph at lines 7--7 []\OT1/pcr/m/n/10.95 sage: show(e37a.plot_Delta(10^6, plot_points=200,[] Overfull \hbox (27.77972pt too wide) in paragraph at lines 7--7 [] \OT1/pcr/m/n/10.95 max_points=100), ymax=0.1, ymin=0, figsize=[10,3])[] Overfull \hbox (61.45703pt too wide) in paragraph at lines 10--11 [][] ) [15 <./graphics/37a-plot_Delta-1000000.png>] [16] [17] (./talk.vrb Overfull \hbox (22.71013pt too wide) in paragraph at lines 21--21 []\OT1/pcr/m/n/10 From: Shigeki Akiyama [] Overfull \hbox (4.71013pt too wide) in paragraph at lines 21--21 []\OT1/pcr/m/n/10 I feel very honored to have your comments on our old[] Overfull \hbox (4.71013pt too wide) in paragraph at lines 21--21 []\OT1/pcr/m/n/10 If we assume Riemann hypothesis for all symmetric L,[] ) [18] [19] (./talk.vrb ) [20 <./graphics/11a-theta-1000000.png>] (./talk.vrb ) [21 <./graphics/37a-theta-1000000.png>] (./talk.vrb ) [22 <./graphics/389a-theta-1000000.png>] (./talk.vrb ) [23 <./graphics/5077a-theta-1000000.png >] (./talk.vrb ) [24 <./graphics/rank4-theta-1000000.png >] (./talk.vrb ) [25 <./graphics/rank5-theta-1000000.png >] (./talk.vrb ) [26 <./graphics/rank6-theta-1000000.png >] (./talk.vrb ) [27 <./graphics/rank7-theta-1000000.png >] (./talk.vrb ) [28 <./graphics/rank8-theta-1000000.png >] (./talk.vrb ) [29 <./graphics/rank28-theta-1000000.p ng>] [30] (./talk.vrb ) [31 <./graphics/rank0-large_cond-fit.p ng>] (./talk.vrb) [32] (./talk.vrb ) [33 <./graphics/rank3-fit-1000000.png>] (./talk.vrb ) [34 <./graphics/rank4-fit.png>] (./talk.vrb ) [35 <./graphics/rank8-fit.png>] (./talk.vrb ) [36 <./graphics/rank28-fit.png>] [37] [38] [39] [40] [41] [42] [43] (./talk.vrb Overfull \hbox (80.33966pt too wide) in paragraph at lines 19--19 []\OT1/pcr/m/n/10.95 curve rank log(R_E(C)) / log(log(C)) for C=10^ 6[] ) [44] (./talk.vrb Overfull \hbox (80.33966pt too wide) in paragraph at lines 16--16 []\OT1/pcr/m/n/10.95 curve rank log(R_E(C)) / log(log(C)) for C=10^ 6[] ) [45] [46] (./talk.aux) ) (see the transcript file for additional information){/usr/share/texmf-texlive/f onts/enc/dvips/base/8r.enc} Output written on talk.pdf (46 pages, 1804946 bytes). Transcript written on talk.log.