CoCalc Public Fileswww / papers / thesis / symbols.tex
Author: William A. Stein
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1% $Header: /home/was/papers/thesis/RCS/symbols.tex,v 1.3 2000/05/11 03:12:03 was Exp$
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3\mbox{}
4\vspace{7ex}
5\section*{\Huge List of Symbols}
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8\begin{tabular}{llr}
9{\bf \large Symbol} \hspace{4em}  & {\bf \large Definition}
10& {\bf \large Page}\\
11&\vspace{-2ex}\\
12$\Adual$  &  dual to $A$ & \pageref{pg:dual}\\
13$\sB_k(N,\eps)$   & module of boundary modular symbols & \pageref{def:boundarysymbols}\\
14$c_A$          & Manin constant of~$A$ & \pageref{defn:maninconstant}\\
15$m_A$ & modular degree & \pageref{defn:modulardegree}\\
16$\e_i$      & $i$th winding element $X^{i-1}Y^{k-2-(i-1)}\{0,\infty\}$
17                  &\pageref{defn:windingelement}\\
18$\sM_k(N,\eps)$& module of modular symbols & \pageref{defn:modsym}\\
19$\esM_k(N,\eps)$& module of extended modular symbols & \pageref{defn:extendedmodsyms}\\
20$M[I]$ & $\intersect_{a\in I} \ker(a)$ & \\
21$P(X,Y)\{\alp,\beta\}$  & higher weight modular symbol & \pageref{pg:higherweightmodsym}\\
22$[P(X,Y),(u,v)]$  & higher weight Manin symbol & \pageref{defn:maninsymbols}\\
23%$R[\eps]$ & $R(\{\eps(a) : a \in \Z/N\Z\})$ & \pageref{defn:keps}\\
24$\sS_k(N,\eps)$& module of cuspidal modular symbols & \pageref{defn:cuspidalmodularsymbols}\\
25$T_n$ & $n$th Hecke operator & \pageref{subsec:heckeonmanin}\\
26$V_k$ & module of homogeneous polynomials of degree~$k$ & \pageref{defn:vk}\\
27$W_d$    & $d$th Atkin-Lehner involution & \pageref{sec:atkin-lehner}\\
28$\alp_t$, $\beta_t$ & degeneracy maps & \pageref{pg:degeneracymaps}\\
29$\Theta_f$  &  rational period mapping  & \pageref{sec:ratperiod}\\
30$\sigma$, $\tau$  & $\sigma=\abcd{0}{-1}{1}{\hfill 0}$,
31                    $\tau=\abcd{0}{-1}{1}{-1}$ & \pageref{defn:sigmatau}\\
32$\Phi_f$ &  analytic period mapping & \pageref{defn:periodmapping}\\
33$\Phi_{A,p}$ & component group of~$A$ at~$p$ & \pageref{defn:componentgroup}\\
34$\Omega_A$ & real volume & \pageref{defn:omega}\\
35$\langle \,\, , \, \rangle$ & integration pairing & \pageref{thm:perfectpairing}\\
36$*$ & star involution & \pageref{sec:starinvolution}\\
37\end{tabular}
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