Geodesic
Functional Equations for Hecke–Maass Series
Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 2, pp. 23-32 Cet article a éte moissonné depuis la source Math-Net.Ru

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The Dirichlet (Hecke–Maass) series associated with the eigenfunctions $f$ and $g$ of the invariant differential operator $\Delta_k=-y^2(\partial^2\!/\partial x^2+\partial^2\!/\partial y^2)+ iky\,\partial/\partial x$ of weight $k$ are investigated. It is proved that any relation of the form $(f|_kM)=g$ for the $k$-action of the group $SL_2(\mathbb{R})$ is equivalent to a pair of functional equations relating the Hecke–Maass series for $f$ and $g$ and involving only traditional gamma factors. 
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V. A. Bykovskii. Functional Equations for Hecke–Maass Series. Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 2, pp. 23-32. http://geodesic.mathdoc.fr/item/FAA_2000_34_2_a2/

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