Abstract: After a short introduction I will focus on the relation between the Riesz and the Baez-Duarte criterion for the Riemann Hypothesis. In particular I will present the relation between the function R(x) appearing in the Riesz criterion and the sequence c_k appearing in the Baez-Duarte formulation. It is shown that R(x) can be expressed by c_k and vice versa the sequence c_k can be obtained from the values of R(x) at integer arguments. Also some relations involving c_k and R(x), in particular the value of the alternating sum of c_k will be given. The presented results were obtained in collaboration with J. Cislo.