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Funktsional. Anal. i Prilozhen., 2000, Volume 34, Issue 2, Pages 23–32 (Mi faa292)  

This article is cited in 1 scientific paper (total in 1 paper)

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.

DOI: https://doi.org/10.4213/faa292

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

Bibliographic databases:

UDC: 511.334+515.178
Received: 29.10.1998

Citation: V. A. Bykovskii, “Functional Equations for Hecke–Maass Series”, Funktsional. Anal. i Prilozhen., 34:2 (2000), 23–32; Funct. Anal. Appl., 34:2 (2000), 98–105

Citation in format AMSBIB
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\paper Functional Equations for Hecke--Maass Series
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\pages 23--32
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\jour Funct. Anal. Appl.
\yr 2000
\vol 34
\issue 2
\pages 98--105
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Diamantis N., Goldfeld D., “A Converse Theorem For Double Dirichlet Series and Shintani Zeta Functions”, J. Math. Soc. Jpn., 66:2 (2014), 449–477  crossref  mathscinet  zmath  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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