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Informally, the Maass–Selberg relations say that the inner product of two distinct
Eisenstein series is zero. However the integral defining the inner product does not converge, so the Eisenstein series first have to be truncated. The Maass–Selberg relations then say that the inner product of two
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generalized the Maass–Selberg relations to
Eisenstein series of higher rank semisimple group (and named the relations after Maass and Selberg) and found some analogous relations between
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Maass, Hans (1949), "Über eine neue Art von nichtanalytischen automorphen
Funktionen und die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen",
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Harish-Chandra (1976), "Harmonic analysis on real reductive groups. III. The Maass-Selberg relations and the
Plancherel formula",
331:, Tata Institute of Fundamental Research Lectures on Mathematics, vol. 29, Bombay: Tata Institute of Fundamental Research,
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truncated
Eisenstein series is given by a finite sum of elementary factors that depend on the truncation chosen, whose
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Harish-Chandra (1972), "On the theory of the
Eisenstein integral", in Gulick, Denny; Lipsman, Ronald L. (eds.),
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introduced the Maass–Selberg relations for the case of real analytic
Eisenstein series on the upper half plane.
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Conference on
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are some relations describing the inner products of truncated
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Proc. Internat. Congr. Mathematicians (Stockholm, 1962)
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extended the relations to symmetric spaces of rank 1.
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Lectures on modular functions of one complex variable
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18:Maass–Selberg relations
403:-related article is a
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16:In mathematics, the
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