In this paper, we propose a general construction for creating statistically random sequences using digit expansions of real functions. We identify different pitfalls and weaknesses in the presented system. A pseudorandom number generator (PRNG) is described based on a modified Riemann-Siegel Z(t) function. It is shown that the output satisfies the statistical requirements of the NIST SP 800-22 randomness suite. We also analyze the resistance of the system against some well-known cryptographic attacks.