PomeRemark 5.16.12.4E2D4F8663A3 This definition is different from a few references, where instead of $\exp (-\varphi )$, they use $\exp (-2\varphi )$. The conventions adopted in the current book are the most convenient ones as far as I know. They simplify a number of formulae. As a mnemonic, for any real $\lambda >0$, we have
\[ \mathcal{I}(\lambda \log |z|^2)=\mathcal{O}_{\mathbb {C}}\left(-\lfloor \lambda \rfloor \{ 0\} \right)\quad \Bigl (\textup{instead of }\mathcal{O}_{\mathbb {C}}\left(-\lfloor 2\lambda \rfloor \{ 0\} \right)\Bigr ), \]
where $z$ is a variable in $\mathbb {C}$ and $\{ 0\} $ is the divisor defined by $0\in \mathbb {C}$.
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