Remarks on `Riemann's example' \(\sum_{n=1}^ \infty {\sin n^ 2x\over n^ 2}\) of a continuous, non-differentiable function
According to Weierstraß Riemann had claimed in his lectures of 1861 that this function was non-differentiable on a dense point set. New sources confirm that both Weierstraß and Kronecker gave proofs, and back up the Riemannian origin of the function. Also, the author gives a proof in the style of Riemann, using information on the growth of the theta series at the boundary of its domain of convergence, as found in a fragment by Riemann.
scientific article; zbMATH DE number 1029202
scientific article