His doctoral thesis Quadratische Formen und Galois-Cohomologie (Quadratic Forms and Galois Cohomology) was supervised by Friedrich Hirzebruch.
Scharlau's research deals with number theory and, in particular, the theory of quadratic forms, about which he wrote a 1985 monograph Quadratic and Hermitian Forms in Springer's series Grundlehren der mathematischen Wissenschaften.
[4][5] Scharlau was also an amateur ornithologist and author of two novels, I megali istoria - die große Geschichte (2nd edition 2001), set on the Greek island of Naxos, and Scharife (2001), set on the island of Zanzibar in the 19th century.
[6] He also deals with the history of mathematics and wrote, with Hans Opolka,[7] a historically-oriented introduction to number theory.
In 1974 he was invited as speaker with talks On subspaces of inner product spaces at the International Congress of Mathematicians in Vancouver.