Dirichlet Series of Modular Forms

  • Anatoli AndrianovEmail author
Part of the Universitext book series (UTX)

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.

Radial Series of Cusp Forms. Let us consider modular forms of the spaces
$$\frak{N}_k^n(q, \chi) =\frak{N}_k\left(\Gamma_0^n(q), {\boldsymbol \chi} \right)$$


Zeta Function Modular Form Fourier Expansion Fundamental Domain Eisenstein Series 
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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Russian Academy of SciencesSteklov Institute of MathematicsPetersburgRussia

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