Some aspects of analytic number theory: parity, transcendence, and multiplicative functions

Questions on parities play a central role in analytic number theory. Properties of the partial sums of parities are intimate to both the prime number theorem and the Riemann hypothesis. This thesis focuses on investigations of Liouville's parity function and related completely multiplicative parity functions. We give results about the partial sums of parities as well as transcendence of functions and numbers associated to parities. For example, we show that the generating function of Liouville's parity function is transcendental over the ring of rational functions with coefficients from a finite field. Within the course of investigation, relationships to finite automata are also discussed.