Speaker:Shigeru Kanemitsu (Kinki University,Japan） Venue: B1044 Time: 2017年09月21日 10:30-11:30 Title: Number theory in the unit disc. Abstract:The Riemann-Bochner-Hecke correspondence refers to the one between the behavior of the modular forms in the upper half-plane and the zeta-functions in the right half-plane. The Lambert series in its power series form is a function in the unit disc and its limiting behavior has been a subject of research. Starting from Wintner's analysis of Riemann's posthumous fragment I, II, we consider the threshold of the functional equation by an intriguing example of Davenport-Chowla's arithmetical Fourier series which has the Liouville function series on one hand and Riemann's example of a continuous nowhere differentiable function on the other. We shall introduce our recent work in this area.