Another Khazar center was established in the Crimea, among Byzantine Greeks and Jews. From the Crimea the Khazars pressed forward in the direction of Byzantium and the Balkan Peninsula, constituting a serious menace to the Roman Empire of the East. As a rule, the Byzantine emperors concluded alliances with the kings, or khagans, of the Khazars, checking their unbridled energy by means of concessions and the payment of tribute. In Constantinople the illusion was fostered that the Church, and with it Byzantine diplomacy, were in the end bound to triumph over all the Khazars--by converting them to Christianity. With this purpose in view, missionaries were dispatched from Byzantium, while the local bishops of Tauris were working zealously to the same end. But the task proved extremely difficult, for the Greek Church found itself face to face with a powerful rival in Judaism, which succeeded in establishing its hold on a part of the Khazar nation. While yet in their pagan state, the Khazars were exposed at one and the same time to the influences of three religions: Mohammedanism, which pursued its triumphant march from the Arabic Caliphate; Christianity, which was spreading in Byzantium, and Judaism, which, headed by the Exilarchs and Gaons of Babylonia, was centered in the Caliphate, while its ramifications spread all over the Empire of Byzantium and its colonies on the Black Sea. The Arabs and the Byzantines succeeded in converting several groups of the Khazar population to Islam and Christianity, but the lion's share fell to Judaism, for it managed to get hold of the royal dynasty and the ruling classes. The conversion of the Khazars to Judaism, which took place about 740, is described circumstantially in the traditions preserved among the Jews and in the accounts of the medieval Arabic travelers: