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Название: Quantization and Non-Holomorphic Modular Forms
Автор: Unterberger A.
Аннотация:
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).
L-function131145 Lax — Phillips theory194 Maass — Hecke forms131 Mehler's formula27 Metaplectic representation119179 Odd zeta series in two variables95112 p-adic calculations168 Petersson space 48 Poisson bracket73 Poisson bracket of Eisenstein series111 Product of Eisenstein series78 Product of Eisenstein series, continuous part of product89 Product of Eisenstein series, continuous part of red. prod.84 Product of Eisenstein series, discrete part of red. prod.101 Quadratic fields216 Radon (dual) transform25 Radon in an -context27 Radon transform425 Rankin — Selberg unfolding method66 Recovering Fourier coefficients of forms66 Reduced Poisson bracket of Eisenstein series111 Reduced product of Eisenstein series8082 Residues (cuspidal)19 Residues of zeta series in two variables141 Resolution of identity121 Roelcke — Selberg expansion55061 Roelcke — Selberg expansion of Poisson bracket145 Roelcke — Selberg expansion of product of Eisenstein series89133138 Roelcke — Selberg expansion of reduced Poisson bracket112 Roelcke — Selberg expansion of reduced product of Eisenstein series84101 Symbolic calculi179 Symplectic Fourier transf.26 Weber — Schafheitlin integral467288105 Weyl calculus33 Wigner function121 Zeros of zeta function97101108151152157 Zeta series in two variables91108 Zeta series in two variables, link with Kloosterman sums93