This is TeX, Version 3.14159 (Web2C 7.4.5) LaTeX2e <2001/06/01> Babel and hyphenation patterns for american, french, german, ngerman, b asque, italian, portuges, russian, spanish, nohyphenation, loaded. (./katz.tex (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2001/04/21 v1.4e Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size11.clo)) (/usr/share/texmf/tex/latex/pstricks/pstricks.sty (/usr/share/texmf/tex/generic/pstricks/pstricks.tex `PSTricks' v97 patch 14 <1999/12/23> (tvz) (/usr/share/texmf/tex/generic/pstricks/pstricks.con))) (/usr/share/texmf/tex/latex/amsmath/amsmath.sty For additional information on amsmath, use the `?' option. 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Missing $ inserted. $ l.173 ...n. Let p=5. I'd love to compute (mod p^ 4 = 725, ! Missing $ inserted. $ l.175 ! Missing $ inserted. $ l.176 1/p U_ p(j-744) ! Missing $ inserted. $ l.177 ! Missing $ inserted. $ l.178 ...l divided by a power of j. Ditto for 1/p^ 2 U_p^2(j-744). ! Missing $ inserted. $ l.181 Overfull \hbox (131.29549pt too wide) in paragraph at lines 178--181 []\OT1/cmr/m/n/10.95 as a poly-no-mial di-vided by a power of j. Ditto for 1/p$ []\OML/cmm/m/it/10.95 U[]\OT1/cmr/m/n/10.95 (\OML/cmm/m/it/10.95 j \OMS/cmsy/m/ n/10.95 ^^@ \OT1/cmr/m/n/10.95 744)\OML/cmm/m/it/10.95 :Dittofor\OT1/cmr/m/n/10 .95 1\OML/cmm/m/it/10.95 =p[]U[]\OT1/cmr/m/n/10.95 (\OML/cmm/m/it/10.95 j \OMS/ cmsy/m/n/10.95 ^^@ \OT1/cmr/m/n/10.95 744)\OML/cmm/m/it/10.95 :\OT1/cmr/m/n/10. 95 (\OML/cmm/m/it/10.95 Untiltheysettledownmod\OT1/cmr/m/n/10.95 725\OML/cmm/m/ it/10.95 :\OT1/cmr/m/n/10.95 )\OML/cmm/m/it/10.95 Infact; thelimit$ ! Missing $ inserted. $ l.182 Lim_ n 1/p^n U_p^n(j-744) ! Missing $ inserted. $ l.183 ! Missing $ inserted. $ l.184 ...e eigenfunction that Gouvea and I call f_ 1 in ! Missing $ inserted. $ l.187 Overfull \hbox (287.54347pt too wide) in paragraph at lines 184--187 []\OT1/cmr/m/n/10.95 exists 5-adically (it is the eigen-func-tion that Gou-vea and I call f$[]\OML/cmm/m/it/10.95 inourpaper\OT1/cmr/m/n/10.95 "\OML/cmm/m/it/ 10.95 Searchingforeigenfunctions\OT1/cmr/m/n/10.95 ")\OML/cmm/m/it/10.95 andhas anexpansionasapolynomialinjplusapowerseriesinj[]:$ ! Missing $ inserted. $ l.193 K := IntegerRing(p^ pow); ! Missing $ inserted. $ l.196 [33] ! Misplaced alignment tab character &. l.200 return & +[Coefficient(f,n*p)*q^n : n in [1..d]] + O(q^(d+1)); ! Missing $ inserted. $ l.200 return &+[Coefficient(f,n*p)*q^ n : n in [1..d]] + O(q^(d+1)); ! Missing $ inserted. $ l.202 Overfull \hbox (53.77173pt too wide) in paragraph at lines 197--202 []\OT1/cmr/m/n/10.95 intrinsic Up(f::RngSerLaurElt) -> RngSer-Lau-rElt d := Fl oor((AbsolutePrecision(f)-1)/p); re-turn +[Coefficient(f,n*p)*q$[] : ! Missing $ inserted. $ l.205 ...turn Max([i : i in [0..pow] | Integers(p^ i)!x eq 0]); ! Missing $ inserted. $ l.207 ! Missing $ inserted. $ l.214 h := j^ r*g; ! Missing $ inserted. $ l.237 Overfull \hbox (31.04933pt too wide) in paragraph at lines 208--237 \OT1/cmr/m/n/10.95 1; while true do print r; h := j$[] \OMS/cmsy/m/n/10.95 ^^C \OML/cmm/m/it/10.95 g\OT1/cmr/m/n/10.95 ; \OML/cmm/m/it/10.95 v \OT1/cmr/m/n/10 .95 := []; \OML/cmm/m/it/10.95 S < X >\OT1/cmr/m/n/10.95 := \OML/cmm/m/it/10.95 PolynomialRing\OT1/cmr/m/n/10.95 (\OML/cmm/m/it/10.95 K\OT1/cmr/m/n/10.95 ); \ OML/cmm/m/it/10.95 F \OT1/cmr/m/n/10.95 := 0; \OML/cmm/m/it/10.95 print\OT1/cmr /m/n/10.95 "\OML/cmm/m/it/10.95 h \OT1/cmr/m/n/10.95 = "\OML/cmm/m/it/10.95 ; h \OT1/cmr/m/n/10.95 ; \OML/cmm/m/it/10.95 print\OT1/cmr/m/n/10.95 "\OML/cmm/m/it /10.95 Valuation\OT1/cmr/m/n/10.95 (\OML/cmm/m/it/10.95 h\OT1/cmr/m/n/10.95 ) = Overfull \hbox (28.70647pt too wide) in paragraph at lines 208--237 \OT1/cmr/m/n/10.95 "\OML/cmm/m/it/10.95 ; Valuation\OT1/cmr/m/n/10.95 (\OML/cmm /m/it/10.95 h\OT1/cmr/m/n/10.95 ); \OML/cmm/m/it/10.95 foriin\OT1/cmr/m/n/10.95 [\OML/cmm/m/it/10.95 Valuation\OT1/cmr/m/n/10.95 (\OML/cmm/m/it/10.95 h\OT1/cm r/m/n/10.95 )\OML/cmm/m/it/10.95 ::\OT1/cmr/m/n/10.95 0]\OML/cmm/m/it/10.95 doA ppend\OT1/cmr/m/n/10.95 ( []\OML/cmm/m/it/10.95 v; Coefficient\OT1/cmr/m/n/10.9 5 (\OML/cmm/m/it/10.95 h; i\OT1/cmr/m/n/10.95 )); \OML/cmm/m/it/10.95 F \OT1/cm r/m/n/10.95 := \OML/cmm/m/it/10.95 F \OT1/cmr/m/n/10.95 + \OML/cmm/m/it/10.95 C oefficient\OT1/cmr/m/n/10.95 (\OML/cmm/m/it/10.95 h; i\OT1/cmr/m/n/10.95 ) \OMS /cmsy/m/n/10.95 ^^C \OML/cmm/m/it/10.95 X[] \OMS/cmsy/m/n/10.95 ^^@ \OML/cmm/m/ it/10.95 i\OT1/cmr/m/n/10.95 ); \OML/cmm/m/it/10.95 print\OT1/cmr/m/n/10.95 "\O ML/cmm/m/it/10.95 F \OT1/cmr/m/n/10.95 = Overfull \hbox (137.45018pt too wide) in paragraph at lines 208--237 \OT1/cmr/m/n/10.95 "\OML/cmm/m/it/10.95 ; h\OT1/cmr/m/n/10.95 ; \OML/cmm/m/it/1 0.95 z \OT1/cmr/m/n/10.95 := \OML/cmm/m/it/10.95 Min\OT1/cmr/m/n/10.95 ([\OML/c mm/m/it/10.95 Val\OT1/cmr/m/n/10.95 (\OML/cmm/m/it/10.95 Coefficient\OT1/cmr/m/ n/10.95 (\OML/cmm/m/it/10.95 h; n\OT1/cmr/m/n/10.95 )) : \OML/cmm/m/it/10.95 ni n\OT1/cmr/m/n/10.95 [1\OML/cmm/m/it/10.95 ::prec\OT1/cmr/m/n/10.95 ]]); \OML/cm m/m/it/10.95 print\OT1/cmr/m/n/10.95 [\OML/cmm/m/it/10.95 Val\OT1/cmr/m/n/10.95 (\OML/cmm/m/it/10.95 Coefficient\OT1/cmr/m/n/10.95 (\OML/cmm/m/it/10.95 h; n\O T1/cmr/m/n/10.95 )) : \OML/cmm/m/it/10.95 nin\OT1/cmr/m/n/10.95 [1\OML/cmm/m/it /10.95 ::prec\OT1/cmr/m/n/10.95 ]]; \OML/cmm/m/it/10.95 ifzgeprecisionthenretur nF; r\OT1/cmr/m/n/10.95 ; \OML/cmm/m/it/10.95 endif\OT1/cmr/m/n/10.95 ; \OML/cm m/m/it/10.95 r \OT1/cmr/m/n/10.95 := ! Missing $ inserted. $ l.244 r := p^ n; ! Misplaced alignment tab character &. l.246 f := & +[(Integers()!(Coefficient(f,m)) div r)*q^m : m in ) ! Missing $ inserted. $ l.172 Overfull \hbox (142.84215pt too wide) in paragraph at lines 238--172 \OML/cmm/m/it/10.95 AbsolutePrecision\OT1/cmr/m/n/10.95 (\OML/cmm/m/it/10.95 f\ OT1/cmr/m/n/10.95 ); \OML/cmm/m/it/10.95 f \OT1/cmr/m/n/10.95 := +[(\OML/cmm/m/ it/10.95 Integers\OT1/cmr/m/n/10.95 ()!(\OML/cmm/m/it/10.95 Coefficient\OT1/cmr /m/n/10.95 (\OML/cmm/m/it/10.95 f; m\OT1/cmr/m/n/10.95 ))\OML/cmm/m/it/10.95 di vr\OT1/cmr/m/n/10.95 ) \OMS/cmsy/m/n/10.95 ^^C \OML/cmm/m/it/10.95 q[] \OT1/cmr /m/n/10.95 : \OML/cmm/m/it/10.95 min\OT1/cmr/m/n/10.95 [\OML/cmm/m/it/10.95 Val uation\OT1/cmr/m/n/10.95 (\OML/cmm/m/it/10.95 f\OT1/cmr/m/n/10.95 )\OML/cmm/m/i t/10.95 ::prec \OMS/cmsy/m/n/10.95 ^^@ \OT1/cmr/m/n/10.95 1]] + \OML/cmm/m/it/1 0.95 O\OT1/cmr/m/n/10.95 (\OML/cmm/m/it/10.95 q[]rec\OT1/cmr/m/n/10.95 ); \OML/ cmm/m/it/10.95 printf\OT1/cmr/m/n/10.95 "1\OML/cmm/m/it/10.95 =p[]rint\OT1/cmr/ m/n/10.95 "146560\OML/cmm/m/it/10.95 =j \OT1/cmr/m/n/10.95 = [34] (./katz.aux) ) (see the transcript file for additional information) Output written on katz.dvi (34 pages, 825368 bytes). Transcript written on katz.log.