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|a 9783540446606
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|a 10.1007/BFb0104036
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|a Unterberger, André.
|e author.
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
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|a Quantization and Non-holomorphic Modular Forms
|h [electronic resource] /
|c by André Unterberger.
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|a 1st ed. 2000.
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|a Berlin, Heidelberg :
|b Springer Berlin Heidelberg :
|b Imprint: Springer,
|c 2000.
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|a X, 258 p.
|b online resource.
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|a text
|b txt
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|a Lecture Notes in Mathematics,
|x 0075-8434 ;
|v 1742
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|a Distributions associated with the non-unitary principal series -- Modular distributions -- The principal series of SL(2, ?) and the Radon transform -- Another look at the composition of Weyl symbols -- The Roelcke-Selberg decomposition and the Radon transform -- Recovering the Roelcke-Selberg coefficients of a function in L 2(???) -- The "product" of two Eisenstein distributions -- The roelcke-selberg expansion of the product of two eisenstein series: the continuous part -- A digression on kloosterman sums -- The roelcke-selberg expansion of the product of two eisenstein series: the discrete part -- The expansion of the poisson bracket of two eisenstein series -- Automorphic distributions on ?2 -- The Hecke decomposition of products or Poisson brackets of two Eisenstein series -- A generating series of sorts for Maass cusp-forms -- Some arithmetic distributions -- Quantization, products and Poisson brackets -- Moving to the forward light-cone: the Lax-Phillips theory revisited -- Automorphic functions associated with quadratic PSL(2, ?)-orbits in P 1(?) -- Quadratic orbits: a dual problem.
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|a This is a new approach to the theory of non-holomorphic modular forms, based on ideas from quantization theory or pseudodifferential analysis. Extending the Rankin-Selberg method so as to apply it to the calculation of the Roelcke-Selberg decomposition of the product of two Eisenstein series, one lets Maass cusp-forms appear as residues of simple, Eisenstein-like, series. Other results, based on quantization theory, include a reinterpretation of the Lax-Phillips scattering theory for the automorphic wave equation, in terms of distributions on R2 automorphic with respect to the linear action of SL(2,Z).
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|a Number theory.
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|a Number Theory.
|0 http://scigraph.springernature.com/things/product-market-codes/M25001
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|a SpringerLink (Online service)
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|t Springer eBooks
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|i Printed edition:
|z 9783662172988
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|i Printed edition:
|z 9783540678618
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|a Lecture Notes in Mathematics,
|x 0075-8434 ;
|v 1742
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|u https://doi.org/10.1007/BFb0104036
|z Full Text via HEAL-Link
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|a ZDB-2-SMA
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|a ZDB-2-LNM
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|a ZDB-2-BAE
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|a Mathematics and Statistics (Springer-11649)
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