Excerpt:
At Halle the direction of Cantor's research turned away from number theory and towards analysis. This was due to Heine, one of his senior colleagues at Halle, who challenged Cantor to prove the open problem on the uniqueness of representation of a function as a trigonometric series. This was a difficult problem which had been unsuccessfully attacked by many mathematicians, including Heine himself as well as Dirichlet, Lipschitz and Riemann. Cantor solved the problem proving uniqueness of the representation by April 1870. He published further papers between 1870 and 1872 dealing with trigonometric series and these all show the influence of Weierstrass's teaching.