We prove that the graded ring of modular forms of weight divisible by 3 is naturally isomorphic to a certain log canonical ring of the associated elliptic modular surface. This extends the Shioda correspondence between weight 3 cusp forms and holomorphic 2-forms.

We investigate the first hitting times to spheres of Brownian motions with constant drifts. In the case when the Brownian motion starts from a point in $\mathbf{R}^{d}$ except for the origin, an explicit formula for the density function of the hitting time has been obtained. When the starting point is the origin, we represent the density function by means of the density of the hitting time of the Brownian motion without the drift.