add definition of elliptic genus

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......@@ -159,6 +159,16 @@ We therefore have
The genus obtained by this power series is called \Index[L-genus@$L$-genus]{$L$-genus}.
It was proven by \textcite{hirzebruch_Lgenus}, that this genus coincides with the signature.
\end{example}
\begin{definition}
A genus $\varphi$ is called an \Index[genus!elliptic]{elliptic genus}, if the corresponding power seires $f(x)=x/Q(x)$ satisfies on of the three equivalent conditions:
\begin{align}
(f')^2 &= 1- 2 \delta \cdot f^2 + \varepsilon \cdot f^4 \\
f(u+v) &= \frac{f(u)f'(v) + f'(u)f(v)}{1- \varepsilon \cdot f(u)^2 f(v)^2} \\
f(2u) &= \frac{2f(u)f'(u)}{1-\varepsilon \cdot f(u)^4}
\end{align}
\end{definition}
% section introduction_by_julian (end)
\section{Ellipctic Genera -- Markus} % (fold)
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