The earliest existing codification of the prayerbook is the Siddur (order) drawn up by Amram Gaon of Sura about 850.
Half a century later the famous Gaon Seadiah, also of Sura, issued his Siddur, in which the rubrical matter is in Arabic. Besides the Siddur, or order for Sabbaths and general use, there is the Mahzor (cycle) for festivals and fasts.
The office of Gaon lasted for something over 400 years, beginning about A.D.
Mahommedan Babylonia (Persia) was the home of the gaonate, the central authority of religious Judaism, whose power transcended that of the secular exilarchate, for it influenced the synagogue far and wide, while the exilarchate was local.
The schismatic Qaraites initiated or rather necessitated a new Hebrew philology, which later on produced Qimhi, the gaon Saadiah founded a Jewish philosophy, the statesman Hasdai introduced a new Jewish culture - and all this under Mahommedan rule.