Dirichlet Series of Modular Forms
2.1 Radial Dirichlet Series
A natural way to approach zeta functions of modular forms is based on consideration of Dirichlet series constructed by means of Fourier coefficients of the forms. As was indicated in the introduction, a right zeta function must have certain analytic properties and an Euler product factorization. Therefore, the choice of appropriate Dirichlet series is motivated by a possibility of their analytic investigation plus a close relation with Euler products. These two features do not necessarily go together.