University of Wroclaw, Wroclaw, Poland
Landsberg studied at the University of Breslau (now University of Wroclaw).
Leipzig University, Leipzig, Germany
Landsberg studied at Leipzig University, receiving his doctorate in mathematics in 1890.
Landsberg studied at the universities of Breslau and Leipzig from 1883 to 1889, receiving his doctorate in mathematics from the former in 1890.
In 1890 Landsberg went to the University of Heidelberg, where he became a privatdozent in mathematics in 1893 and an extraordinary professor in 1897. He returned to Breslau in this capacity in 1904, but in 1906 he accepted an offer from the University of Kiel, where he was appointed professor ordinarius in 1911. He remained at Kiel until his death.
Landsberg investigated the theory of algebraic functions of two variables, which was then a hardly accessible subject that did not attain its major successes until much later. He also considered the theory of curves in higher-dimensional manifolds and its connection with the calculus of variations and the mechanics of rigid bodies. In addition, he studied theta functions and Gaussian sums. In this work, he touched on the ideas of Weierstrass, Riemann, and Weber. His most important work, however, was his contribution to the development of the theory of algebraic functions of a single variable. Here he studied the Riemann-Roch theorem.
He was able to combine Riemann's function theoretic approach with the Italian geometric approach and with the Weierstrass arithmetical approach. His arithmetic setting of this result led eventually to the modern abstract theory of algebraic functions.
One of his most important works was Theorie der algebraischen Funktionen einer Varaiblen which he wrote jointly with Kurt Hensel. This work remained the standard text on the subject for many years.
It is not known whether Landsberg was married or not.