Let f(n) be an arithmetic function and let h = f*u, where u is the unit function. Assume that the Dirichlet series of f(n) is D(f, s) = 5(38) 5(s) where (s) is the Riemann zeta function 5(8) = - II (1 p)? n=1 P prime (a) Show that D(f,5) = II 9 II (). P prime where g(x) = (3.3% 2:38+1) = 1 + 2013 24 + 2,6 2? +.... k=0 [4] (b) Show that f is a multiplicative function. [2] (c) Use part (a) and part (b) to find the value of f(120) explicitly. [4] (d) Find the Dirichlet series of h. [4] Let f(n) be an arithmetic function and let h = f*u, where u is the unit function. Assume that the Dirichlet series of f(n) is D(f, s) = 5(38) 5(s) where (s) is the Riemann zeta function 5(8) = - II (1 p)? n=1 P prime (a) Show that D(f,5) = II 9 II (). P prime where g(x) = (3.3% 2:38+1) = 1 + 2013 24 + 2,6 2? +.... k=0 [4] (b) Show that f is a multiplicative function. [2] (c) Use part (a) and part (b) to find the value of f(120) explicitly. [4] (d) Find the Dirichlet series of h. [4]