Let w=(w_1, . . . , w_d) be an ordered d-tuple of positive real numbers such that w_1+...+w_d=1 and w_1 \geq ... \geq w_d. A
d-dimensional vector (x_1, . . . , x_q) in R^d is said to be w-singular if for every epsilon for all large enough T there are solutions p in Z^d and q in {1,...,T} such that |qx_i - p_i| < epsilon T^{-w_i} for all i. It was shown by Liao, Shi, Solan, and Tamam that the Hausdorff dimension of 2-dimensional weighted singular vectors is 2-1/(1+w_1). In this talk, we discuss a lower bound of the Hausdorff dimension of d-dimensional weighted singular vectors. This is a joint work with Jaemin Park.
