Study of Eisenstein series and related Dirichlet series

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We study several Dirichlet series associated to modular forms of degree one or two. First, we discovered a new application of Koecher-Maass series of Siegel modular forms. Namely we got a new proof of recent result of Kohnen and Martin on a characterization of degree 2 Siegel cusp forms by the growth of their Fourier coefficients. Our main tools are Koecher-Maass series. Second, we gave some new construction of holomorphic kernel functions of modular L-functions. Using this, we can compute special L-values numericallyrather easily .