Complex continued fractions: early work of the brothers Adolf and Julius Hurwitz

The two brothers Julius and Adolf Hurwitz were born in the middle of the nineteenth century in a small town near Hanover (not far from Göttingen). Already during their schooldays, the two of them became acquainted with mathematical problems and both started to study mathematics, but while the younger brother Adolf turned out to be extremely successful in his research, the elder brother and his work seem to be almost forgotten. This paper examines the lives and works of the two brothers with particular emphasis on the contributions of Julius Hurwitz, and the subsequent reception of their research. It deals with the development of an arithmetical theory for complex continued fractions by Julius and Adolf Hurwitz around 1890 and its rediscovery in the twentieth century.