>>599
>Lemma 7.4. ([EtTh, Proposition 1.4])

追加
q-parameters の定義の明記がないな
まあ、q := e^2πiτかな？

http://www.kurims.kyoto-u.ac.jp/~motizuki/The%20Etale%20Theta%20Function%20and%20its%20Frobenioid-theoretic%20Manifestations.pdf
THE ETALE THETA FUNCTION AND ´
ITS FROBENIOID-THEORETIC MANIFESTATIONS
Shinichi Mochizuki
December 2008
P20
Proposition 1.4. (Relation to the Classical Theta Function)
so Θ¨ extends uniquely to a meromorphic function on Y¨ [cf., e.g., [Mumf ], pp.306-307].

[Mumf] D. Mumford, An Analytic Construction of Degenerating Abelian Varieties over Complete Rings, Appendix to [FC].