This is TeX, Version 3.14159 (Web2C 7.3.1) (format=latex 2000.7.19) 16 APR 2002 13:26 **dsw.tex (dsw.tex LaTeX2e <1999/12/01> patch level 1 Babel and hyphenation patterns for american, french, german, ngerman, i talian, nohyphenation, loaded. (/usr/share/texmf/tex/latex/amscls/amsart.cls Document Class: amsart 2000/01/17 v2.03 \linespacing=\dimen102 \normalparindent=\dimen103 \normaltopskip=\skip41 (/usr/share/texmf/tex/latex/amsmath/amsmath.sty Package: amsmath 2000/01/15 v2.05 AMS math features \@mathmargin=\skip42 For additional information on amsmath, use the `?' option. 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LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 93. LaTeX Font Info: ... okay on input line 93. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 93. LaTeX Font Info: ... okay on input line 93. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 93. LaTeX Font Info: ... okay on input line 93. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 93. LaTeX Font Info: ... okay on input line 93. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 93. LaTeX Font Info: ... okay on input line 93. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 93. LaTeX Font Info: ... okay on input line 93. LaTeX Font Info: Checking defaults for OT2/cmr/m/n on input line 93. LaTeX Font Info: Try loading font information for OT2+cmr on input line 93. (/usr/share/texmf/tex/latex/cyrillic/ot2cmr.fd File: ot2cmr.fd 1999/06/24 v3.2b Computer Modern Cyrillic font definitions ) LaTeX Font Info: ... okay on input line 93. LaTeX Font Info: Try loading font information for U+msa on input line 93. (/usr/share/texmf/tex/latex/amsfonts/umsa.fd File: umsa.fd 1995/01/05 v2.2e AMS font definitions ) LaTeX Font Info: Try loading font information for U+msb on input line 93. (/usr/share/texmf/tex/latex/amsfonts/umsb.fd File: umsb.fd 1995/01/05 v2.2e AMS font definitions ) Underfull \hbox (badness 1953) in paragraph at lines 117--117 [][]\OT1/cmr/m/it/8 Key words and phrases.\OT1/cmr/m/n/8 modular form, $\OML/cm m/m/it/8 L$\OT1/cmr/m/n/8 -function, vis-i-bil-ity, Bloch-Kato con-jec-ture, [] LaTeX Font Info: Try loading font information for U+euf on input line 157. (/usr/share/texmf/tex/latex/amsfonts/ueuf.fd File: ueuf.fd 1995/01/05 v2.2e AMS font definitions ) LaTeX Font Info: Try loading font information for OT2+wncyr on input line 17 4. (/usr/share/texmf/tex/latex/cyrillic/ot2wncyr.fd File: ot2wncyr.fd 1999/05/31 v3.2 Computer Modern Cyrillic font definitions ) [1] [2] [3] Package amsmath Warning: Foreign command \over; (amsmath) \frac or \genfrac should be used instead (amsmath) on input line 330. Overfull \hbox (1.76784pt too wide) in paragraph at lines 356--366 []$[][]$ \OT1/cmr/m/n/10 may be cal-cu-lated as the de-ter-mi-nant of the pe-ri od map from $\OML/cmm/m/it/10 F[]V[] \OMS/cmsy/m/n/10 [] [4] Overfull \hbox (5.33505pt too wide) in paragraph at lines 417--419 \OT1/cmr/bx/n/10 Lemma 4.5. $[][]\OT1/cmr/m/n/10 (#^^@[](\OML/cmm/m/it/10 j\OT1 /cmr/m/n/10 )) = 0$ \OT1/cmr/m/it/10 if $\OML/cmm/m/it/10 A\OT1/cmr/m/n/10 [\OM L/cmm/m/it/10 ^^U\OT1/cmr/m/n/10 ]$ \OT1/cmr/m/it/10 is an ir-re-ducible rep-re -sen-ta-tion of $[]\OT1/cmr/m/n/10 ([]\OML/cmm/m/it/10 =\U/msb/m/n/10 Q\OT1/cmr /m/n/10 )$\OT1/cmr/m/it/10 . [] [5] [6] Overfull \hbox (12.70718pt too wide) in paragraph at lines 574--583 \OT1/cmr/m/n/10 ducibil-ity, $\OML/cmm/m/it/10 H[]\OT1/cmr/m/n/10 (\U/msb/m/n/1 0 Q\OML/cmm/m/it/10 ; A\OT1/cmr/m/n/10 [\U/euf/m/n/10 q\OT1/cmr/m/n/10 ](\OML/c mm/m/it/10 k=\OT1/cmr/m/n/10 2))$ is triv-ial, so $\OML/cmm/m/it/10 H[]\OT1/cmr /m/n/10 (\U/msb/m/n/10 Q\OML/cmm/m/it/10 ; A\OT1/cmr/m/n/10 [\U/euf/m/n/10 q\OT 1/cmr/m/n/10 ](\OML/cmm/m/it/10 k=\OT1/cmr/m/n/10 2))$ in-jects into $\OML/cmm/ m/it/10 H[]\OT1/cmr/m/n/10 (\U/msb/m/n/10 Q\OML/cmm/m/it/10 ; A[]\OT1/cmr/m/n/1 0 (\OML/cmm/m/it/10 k=\OT1/cmr/m/n/10 2))$, [] Underfull \vbox (badness 1226) has occurred while \output is active [] [7] Underfull \vbox (badness 1231) has occurred while \output is active [] [8] Overfull \hbox (1.97449pt too wide) in paragraph at lines 713--727 \OT1/cmr/m/n/10 The Ga-lois or-bits are or-dered first by the de-gree of $\U/ms b/m/n/10 Q\OT1/cmr/m/n/10 ([] \OML/cmm/m/it/10 ; a[]; []\OT1/cmr/m/n/10 )$, the n by $\OMS/cmsy/m/n/10 j[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 a[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 g\OT1/cmr/m/n/10 ))\OMS/cmsy/m/n/10 j$ [] [9] [10] [11] [12] Overfull \hbox (4.50038pt too wide) in paragraph at lines 1006--1006 []\OT1/cmr/m/sc/8 University of Sheffield, De-part-ment of Pure Math-e-mat-ics, Hicks Build-ing, Hounsfield [] [13] [14] (dsw.aux) ) Here is how much of TeX's memory you used: 1724 strings out of 20898 17925 string characters out of 196686 69015 words of memory out of 350001 4506 multiletter control sequences out of 10000+15000 13615 words of font info for 52 fonts, out of 400000 for 1000 175 hyphenation exceptions out of 1000 34i,17n,32p,260b,410s stack positions out of 1500i,100n,500p,50000b,4000s Output written on dsw.dvi (14 pages, 72772 bytes).