This is TeX, Version 3.14159 (Web2C 7.3.1) (format=tex 2000.3.7)  20 JUL 2000 17:42
**\nonstopmode\input modsyms.tex
(modsyms.tex
! Undefined control sequence.
l.1 \comment
            {
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.29 \chapter
             {Modular symbols}%
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.30 \label
           {chap:modsym}\index{Modular symbols}%
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.30 \label{chap:modsym}\index
                              {Modular symbols}%
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.33 $H_1(X_0(N),\Z
                   )$ of the Riemann surface $X_0(N)$.  This presentation
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.36 ... a basis for the space $S_2(\Gamma_0(N),\C
                                                  )$ of cusp
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.40 Sections~\ref
                  {sec:defnofmodsyms}--\ref{cuspidalsymbols}.  Then in
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.40 Sections~\ref{sec:defnofmodsyms}--\ref
                                           {cuspidalsymbols}.  Then in
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.41 Section~\ref
                 {sec:duality}, we review the
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.43 In Section~\ref
                    {sec:heckeops}, we see that
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.46 Section~\ref
                 {sec:degeneracymaps} we see that the same is true of the
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.47 degeneracy maps.  Section~\ref
                                   {sec:maninsymbols} describes Manin
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.49 modular symbols.  Finally, Section~\ref
                                            {sec:tori} introduces the
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.64 ...enced by the publications of Cremona~\cite
                                                  {cremona:gammaone,
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.65 cremona:algs}\index
                        {Cremona} and Merel~\cite{merel:1585}\index{Merel},
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.65 cremona:algs}\index{Cremona} and Merel~\cite
                                                 {merel:1585}\index{Merel},
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.65 ...Cremona} and Merel~\cite{merel:1585}\index
                                                  {Merel},
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.67 Manin~\cite
                {manin:parabolic}, Mazur~\cite{mazur:arithmetic_values,
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.67 Manin~\cite{manin:parabolic}, Mazur~\cite
                                              {mazur:arithmetic_values,
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   _
l.67 ...:parabolic}, Mazur~\cite{mazur:arithmetic_
                                                  values,
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Extra }, or forgotten $.
l.68 mazur:symboles}
                    , and Shokurov~\cite{sokurov:modsym}.  Cremona's
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Undefined control sequence.
l.68 mazur:symboles}, and Shokurov~\cite
                                        {sokurov:modsym}.  Cremona's
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.69 book~\cite
               {cremona:algs} provides a motivated roadmap that guides the
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.71 context of elliptic curves, and Merel's\index
                                                  {Merel} article provides a...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \par 
l.75 
     
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.


Overfull \hbox (1638.86664pt too wide) in paragraph at lines 63--75
\tenrm con-tri-bu-tions of Manin manin:parabolic, Mazur mazur:arithmetic$[]\ten
i alues; mazur \tenrm : \teni symboles; andShokurov []:Cremona[]sbook []provide
samotivatedroadmapthatguidesthereaderwhowishestocomputewithmodularsymbolsinthef
amiliarcontextofellipticcurves; andMerel[]s[]articleprovidesanaccessibleovervie
woftheactionofHeckeoperatorsonhigherweightmodularsymbols; andtheconnectionbetwe
enmodularsymbolsandrelatedcohomologytheories:$ |

\hbox(7.51782+1.94444)x469.75499, glue set - 1.0
.\tenrm c
.\tenrm o
.\discretionary replacing 2
..\tenrm n
..\tenrm -
.\tenrm n
.\kern-0.27779
.etc.

! Undefined control sequence.
l.76 \section
             {The definition of modular symbols}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.77 \label
           {sec:defnofmodsyms}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.80   $$\eps
             :(\Z/N\Z)^*\ra\C^*$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.80   $$\eps:(\Z
                 /N\Z)^*\ra\C^*$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.80   $$\eps:(\Z/N\Z
                     )^*\ra\C^*$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.80   $$\eps:(\Z/N\Z)^*\ra
                           \C^*$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.80   $$\eps:(\Z/N\Z)^*\ra\C
                             ^*$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Double superscript.
l.80   $$\eps:(\Z/N\Z)^*\ra\C^
                              *$$
I treat `x^1^2' essentially like `x^1{}^2'.

! Undefined control sequence.
<recently read> \eps 
                     
l.81 such that $\eps
                    (-1)=(-1)^k$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.82 We call~$N$ the \defn
                          {level}\index{Level of modular symbols|textit},~$k...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.82 We call~$N$ the \defn{level}\index
                                       {Level of modular symbols|textit},~$k...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.83 \defn
          {weight}\index{Weight of modular symbols|textit},
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.83 \defn{weight}\index
                        {Weight of modular symbols|textit},
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
<recently read> \eps 
                     
l.84 and~$\eps
              $ the \defn{Dirichlet character}.\index{Dirichlet character|te...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.84 and~$\eps$ the \defn
                         {Dirichlet character}.\index{Dirichlet character|te...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.84 ...eps$ the \defn{Dirichlet character}.\index
                                                  {Dirichlet character|textit}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.88 $\{\alp
            ,\beta\}$, with $\alp, \beta\in\P^1(\Q)=\Q\union\{\infty\}$,
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
<recently read> \alp 
                     
l.88 $\{\alp,\beta\}$, with $\alp
                                 , \beta\in\P^1(\Q)=\Q\union\{\infty\}$,
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.88 $\{\alp,\beta\}$, with $\alp, \beta\in\P^1(\Q
                                                  )=\Q\union\{\infty\}$,
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.88 ...,\beta\}$, with $\alp, \beta\in\P^1(\Q)=\Q
                                                  \union\{\infty\}$,
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.88 ...\}$, with $\alp, \beta\in\P^1(\Q)=\Q\union
                                                  \{\infty\}$,
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.90   $$\{\alp
               ,\beta\}+\{\beta,\gamma\}+\{\gamma,\alp\} = 0,$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.90 ...alp,\beta\}+\{\beta,\gamma\}+\{\gamma,\alp
                                                  \} = 0,$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
<recently read> \alp 
                     
l.91 for all $\alp
                  ,\beta,\gamma\in\P^1(\Q)$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.91 for all $\alp,\beta,\gamma\in\P^1(\Q
                                         )$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
<recently read> \sM 
                    
l.92 Let $\sM
             $ be the torsion-free quotient of this group by its torsion
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
<recently read> \sM 
                    
l.93 subgroup.  Because $\sM
                            $ is torsion free, $\{\alp,\alp\}=0$ and
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.93 ...p.  Because $\sM$ is torsion free, $\{\alp
                                                  ,\alp\}=0$ and
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.93 ...ecause $\sM$ is torsion free, $\{\alp,\alp
                                                  \}=0$ and
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.94 $\{\alp
            ,\beta\} = -\{\beta,\alp\}$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.94 $\{\alp,\beta\} = -\{\beta,\alp
                                    \}$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.95 \index
           {Modular symbols!relations satisfied by}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.97 \begin
           {remark}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.99 $\{\alp
            ,\beta\}$ as the homology class of an appropriate
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

[1] )
(\end occurred inside a group at level 1)
Output written on modsyms.dvi (1 page, 5360 bytes).