= Hecke operator on marked lattices
{c}
{title2=$T_pF(L,t)=p^{-1}\sum_{L'}F(L',t\bmod L')$}
= Hecke operators on marked lattices
{c}
{synonym}
Sum over index-$p$ overlattices in which the marked point retains exact order $N$. There are $p+1$ summands at good primes and $p$ at bad primes. With homogeneity $F(uL,ut)=u^{-k}F(L,t)$, the coefficient $1/p$ is the normalization giving the standard <Hecke operator> Fourier action. <Cusp holomorphy under rational slash operators> proves preservation of <modular forms>.
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