Fractal dimensions of the graph and level sets of the Riemann-Rademacher functions

Let Rs(x)=& sum;(infinity)(i=1)i(-s)R(i)(x) be the Riemann-Rademacher functions, where s>1 and {Ri(x)}i=1 infinity is the classical Rademacher function system. In this paper, we prove that both the box and Assouad dimensions of the graph of R-s(x) are equal to 2. We also study the Hausdorff dimension of the graph and level sets of R-s(x), by constructing a new sequence of Rademacher functions R-s,R-n(x), and based on the absolute continuity of their distribution functions and the L-p-norm (0<p <=+infinity) uniform boundedness of density functions.