Journal of Lie Theory

no. 4
On the Inner Product of Certain Automorphic Forms and Applications
Journal of Lie Theory, Volume 22 (2012) no. 4, pp. 1091-1107
\def\R{{\Bbb R}} Let $\Gamma\subset {\rm SL}_2(\R)$ be a discrete subgroup such that the quotient $\Gamma\backslash{\rm SL}_2(\R)$ has a finite volume. In this paper we compute the Petersson inner product of automorphic cuspidal forms with Poincar\' e series constructed out of matrix coefficients of a holomorphic discrete series of lowest weight $m\ge 3$. We apply the result to give new and representation-theoretic proofs of previous results, some of which were known to Petersson, and are anyway not surprising to experts.
DOI: 10.5802/jolt.707
Classification: 11F70, 11F20
Keywords: Fuchsian groups, automorphic forms, modular forms, Poincare series 
@article{JOLT_2012_22_4_a8,
     author = {G. Muic},
     title = {On the {Inner} {Product} of {Certain} {Automorphic} {Forms} and {Applications}},
     journal = {Journal of Lie Theory},
     pages = {1091--1107},
     year = {2012},
     volume = {22},
     number = {4},
     doi = {10.5802/jolt.707},
     zbl = {1275.11069},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.707/}
}
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G. Muic. On the Inner Product of Certain Automorphic Forms and Applications. Journal of Lie Theory, Volume 22 (2012) no. 4, pp. 1091-1107. doi: 10.5802/jolt.707

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