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Functional equations for Hecke-Maaass series

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Abstract

The Dirichlet (Hecke-Maass) series associated with the eigenfuctionsf andg of the invariant differential operator Δk=−y2(∂2/∂x2)+iky∂/∂x of weightk are investigated. It is proved that any relation of the form (f/kM)=g for thek-action of the groupSL 2 SL 2(ℝ) is equivalent to a pair of functional equations relating the Hecke-Maass series forf andg and involving only traditional gamma factors.

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Authors
  1. V. A. Bykovskii
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Additional information

This work was supported by the Russian Foundation for Basic Research (grant No. 96-01-10439).

Institute of Applied Mathematics, Far East Division of Russian Academy of Sciences. Translated from Funktional'nyi Analiz i Ego Prilozheniya, Vol. 34, No. 2, pp. 23–32, April–June, 2000.

Translated by V. M. Volosov

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Bykovskii, V.A. Functional equations for Hecke-Maaass series. Funct Anal Its Appl 34, 98–105 (2000). https://doi.org/10.1007/BF02482422

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  • DOI: https://doi.org/10.1007/BF02482422

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