This is TeX, Version 3.14159 (Web2C 7.3.1) (format=latex 2002.4.12) 5 JUN 2002 10:34 **dsw3.tex (dsw3.tex LaTeX2e <2000/06/01> Babel and hyphenation patterns for american, french, german, ngerman, i talian, nohyphenation, loaded. (/usr/share/texmf/tex/latex/amscls/amsart.cls Document Class: amsart 2000/10/26 v2.08 \linespacing=\dimen102 \normalparindent=\dimen103 \normaltopskip=\skip41 (/usr/share/texmf/tex/latex/amsmath/amsmath.sty Package: amsmath 2000/07/18 v2.13 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 158. (/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 5. (/usr/share/texmf/tex/latex/cyrillic/ot2wncyr.fd File: ot2wncyr.fd 1999/12/17 v3.2a 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 332. [4] Overfull \hbox (5.33505pt too wide) in paragraph at lines 427--429 \OT1/cmr/bx/n/10 Lemma 4.6. $[][]\OT1/cmr/m/n/10 (#^^@[](\OML/cmm/m/it/10 j\OT1 /cmr/m/n/10 )) = 0$ \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 (4.7741pt too wide) in paragraph at lines 574--584 \OT1/cmr/m/it/10 has di-men-sion $\OML/cmm/m/it/10 r > \OT1/cmr/m/n/10 0$\OT1/c mr/m/it/10 . Sup-pose that $\OML/cmm/m/it/10 A\OT1/cmr/m/n/10 [\U/euf/m/n/10 q\ OT1/cmr/m/n/10 ]$ \OT1/cmr/m/it/10 is an ir-re-ducible rep-re-sen-ta-tions of $ []\OT1/cmr/m/n/10 ([]\OML/cmm/m/it/10 =\U/msb/m/n/10 Q\OT1/cmr/m/n/10 )$ [] [7] Overfull \hbox (38.38492pt too wide) in paragraph at lines 627--654 \OT1/cmr/m/n/10 since this would im-ply that the nat-u-ral map from $\OML/cmm/m /it/10 H[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 I[]; V[]\OT1/cmr/m/n/10 (\OML/cmm/m /it/10 k=\OT1/cmr/m/n/10 2))$ to $\OML/cmm/m/it/10 H[]\OT1/cmr/m/n/10 (\OML/cmm /m/it/10 I[]; A[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 k=\OT1/cmr/m/n/10 2))$ [] [8] [9] [10] [11] Underfull \vbox (badness 2189) has occurred while \output is active [] [12] [13] Overfull \hbox (4.50038pt too wide) in paragraph at lines 1041--1041 []\OT1/cmr/m/sc/8 University of Sheffield, De-part-ment of Pure Math-e-mat-ics, Hicks Build-ing, Hounsfield [] [14] (dsw3.aux) ) Here is how much of TeX's memory you used: 1736 strings out of 20887 18112 string characters out of 196274 70569 words of memory out of 350001 4530 multiletter control sequences out of 10000+15000 13310 words of font info for 51 fonts, out of 400000 for 1000 175 hyphenation exceptions out of 10000 34i,17n,32p,295b,419s stack positions out of 3000i,100n,1500p,50000b,4000s Output written on dsw3.dvi (14 pages, 76540 bytes).