This article is cited in 6 papers

Functional Equations for Hecke–Maass Series

V. A. Bykovskii

Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences

Abstract: 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.

UDC: 511.334+515.178

Received: 29.10.1998

DOI: 10.4213/faa292

 English version: Functional Analysis and Its Applications, 2000, 34:2, 98–105

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