Let \(R^{s}(x)=\sum _{i=1}^\infty {{i^{-s}}}R_{i}(x)\) be the Riemann-Rademacher functions, where \(s>1\) and \({\lbrace R_{i}(x)\rbrace }_{i=1}^{\infty }\) 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 \(R_{s,n}(x)\) , and based on the absolute continuity of their distribution functions and the \(L^p\) -norm \((0<p\le +\infty )\) uniform boundedness of density functions.
