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The Eastern Roman Empire – today conventionally named the Byzantine Empire, a name not in use during its own time – became increasingly influenced by Greek culture after the 7th century, when Emperor Heraclius (AD 575 - 641) decided to make Greek the empire's official language. Certainly from then on, but likely earlier, the Roman and Greek cultures were virtually fused into a single Greco-Roman world. Although the Latin West recognized the Eastern Empire's claim to the Roman legacy for several centuries, after Pope Leo III crowned Charlemagne, king of the Franks, as the "Roman Emperor" on 25 December 800, an act which eventually led to the formation of the Holy Roman Empire, the Latin West started to favour the Franks and began to refer to the Eastern Roman Empire largely as the Empire of the Greeks (Imperium Graecorum).

What decision did he make that influenced the culture in an attempt to make things more homogeneous ?
decided to make Greek the empire's official language.