Multiplicative number theory with applications to modular forms and enumeration of groups

In this thesis we apply techniques of Multiplicative Number Theory such as sieves with weights, generating functions and Euler products to approach certain problems in the theory of modular forms and the enumeration of finite groups. In the first Chapter we consider the problem of finding upper bounds for the gap function of the Fourier expansion of certain modular forms. Second Chapter is devoted to short interval results on the local density of prime independent multiplicative functions. In the final Chapter we obtain lower bounds on the number of conjugacy classes of a finite-group for almost all group orders.