Abstract
We give a sufficient condition of bounded growth for the non-holomorphic Eisenstein series on SL 2(ℤ). The C ∞-automorphic forms of bounded growth are introduced by Sturm (Duke Math. J. 48(2), 327–350, 1981) in the study of automorphic L-functions. We also give a Laplace-Mellin transform of the Fourier coefficients of the Eisenstein series. The transformation constructs a projection of the Eisenstein series to the space of holomorphic cusp forms.
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