CoCalc Public Fileswww / papers / thesis-old / symbols.tex
Author: William A. Stein
Compute Environment: Ubuntu 18.04 (Deprecated)
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2\vspace{7ex}
3\section*{\Huge List of Symbols}
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6\begin{tabular}{llr}
7{\bf \large Symbol} \hspace{4em}  & {\bf \large Definition}
8& {\bf \large Page}\\
9&\vspace{-2ex}\\
10$\Adual$  &  dual of $A$ & \pageref{pg:dual}\\
11$\sB_k(N,\eps)$   & boundary modular symbols & \pageref{def:boundarysymbols}\\
12$c_A$          & Manin index of~$A$ & \pageref{defn:maninconstant}\\
13$\delta_A$ & modular degree & \pageref{defn:modulardegree}\\
14$\e$      & winding element $\e=\{0,\infty\}$ &\pageref{defn:windingelement}\\
15$\sM_k(N,\eps;K)$& modular symbols & \pageref{defn:modsym}\\
16$\esM_k(N,\eps;K)$& extended modular symbols & \pageref{defn:extendedmodsyms}\\
17$M[I]$ & $\intersect_{a\in I} \ker(a)$ & \\
18$P(X,Y)\{\alp,\beta\}$  & higher weight modular symbol & \pageref{pg:higherweightmodsym}\\
19$[P(X,Y),(u,v)]$  & higher weight Manin symbol & \pageref{defn:maninsymbols}\\
20%$R[\eps]$ & $R(\{\eps(a) : a \in \Z/N\Z\})$ & \pageref{defn:keps}\\
21$\Sha(A/K)^{\circ}$ & visible part of~$\Sha$ & \pageref{defn:visiblepart}\\
22$\sS_k(N,\eps;K)$& cuspidal modular symbols & \pageref{defn:cuspidalmodularsymbols}\\
23$T_n$ & $n$th Hecke operator & \pageref{subsec:heckeonmanin}\\
24$V_k$ & homogeneous polys. of degree $k$ in $\Z[X,Y]$ & \pageref{defn:vk}\\
25$W_n$    & $n$th Atkin-Lehner involution & \pageref{sec:atkin-lehner}\\
26$\cX_p(M)$ & character group of torus of $J_0(pM)$ at~$p$ & \pageref{defn:chargroup}\\
27$\alp_t$, $\beta_t$ & degeneracy maps & \pageref{pg:degeneracymaps}\\
28$\Theta_f$  &  rational period mapping  & \pageref{sec:ratperiod}\\
29$\sigma$, $\tau$  & $\sigma=\abcd{0}{-1}{1}{\hfill 0}$,
30                    $\tau=\abcd{0}{-1}{1}{-1}$ & \pageref{defn:sigmatau}\\
31$\Phi_f$ &  analytic period mapping & \pageref{defn:periodmapping}\\
32$\Phi_{A,p}$ & component group of~$A$ at~$p$ & \pageref{defn:componentgroup}\\
33$\Omega_A$ & real volume & \pageref{defn:omega}\\
34$\langle \,\, , \, \rangle$ & integration pairing & \pageref{thm:perfectpairing}\\
35$*$ & conjugation involution & \pageref{sec:starinvolution}\\
36\end{tabular}
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