www.kurims.kyoto-u.ac.jp/~gokun/DOCUMENTS/abc_ver6.pdf 山下剛サーベイ A PROOF OF ABC CONJECTURE AFTER MOCHIZUKI GO YAMASHITA Date: August 31, 2017. P25 where qE,v = e^2πiτv and τv is in the upper half plane. P94 Lemma 7.4. ([EtTh, Proposition 1.4]) Put where q := e^2πiτ , and U¨ := e^πiz)