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140122 ||| eng |
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|a 9783540446606
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|a Unterberger, André
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|a Quantization and Non-holomorphic Modular Forms
|h Elektronische Ressource
|c by André Unterberger
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|a 1st ed. 2000
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| 260 |
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|a Berlin, Heidelberg
|b Springer Berlin Heidelberg
|c 2000, 2000
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| 300 |
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|a X, 258 p
|b online resource
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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 Number theory
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| 653 |
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|a Number Theory
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|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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|a Lecture Notes in Mathematics
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|a 10.1007/BFb0104036
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|u https://doi.org/10.1007/BFb0104036?nosfx=y
|x Verlag
|3 Volltext
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|a 512.7
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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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