In one or two paragraphs, respond to this prompt: how did byzantine culture influence europe?

Through the Justinian Code. 
This was a codification into a single volume of all then existing Roman Law by the Byzantine emperor Justinian between 529 and 534.Throughout the Middle Ages (and in some cases well beyond) most European Medieval law was based on the Code,and kings and other Western rulers used laws to legitimize both their rule and laws and policies they introduced. 

Crusaders that came into contact with the Byzantines during the Crusades made a careful study of their fortifications,which were different to castles in Europe at the time.New ideas gained from this contact were transmitted back to Europe,and incorporated into new castles built in Europe.A good example is Chateau Gaillard,built by Richard I of England in France between 1196 and 1198.It clearly incorporates Byzantine features not previously used in Western European castles,and soon all castles in Western Europe were being built on the same principles. 

Western European knights and heavy cavalry were using spears,which could be used for thrusting or throwing,from horseback up to the mid 11th century.Norman adventurers in Italy came into combat with Byzantine heavy cavalry armed with the lance,and were heavily defeated - Norman knights at Cannae in 1018 were ridden down by the Byzantines in an early example of this.However,returning Normans introduced the lance to Normandy,and gradually most Norman knights adopted the couched lance as their main battle weapon.The Bayeux Tapestry shows that by 1066,the transition from spear to lance was almost complete - a few knights are still using spears,which they are depicted as throwing (or about to throw);the majority of Norman knights in the Tapestry are using couched lances.The use of the lance then spread from Norman knights to other knights across the whole of Europe.