Unterberger A. — Quantization and Non-Holomorphic Modular Forms :: Электронная библиотека попечительского совета мехмата МГУ

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Unterberger A. — Quantization and Non-Holomorphic Modular Forms

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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).

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 253

Добавлена в каталог: 31.10.2008

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Предметный указатель

$C^{\infty}$ -vectors of $\pi_{\nu}$       12
Analytic continuation of zeta series $\zeta_{n}$ in two variables      108 112
Asymptotics of composition      189
Automorphic distribution      126
Automorphic function      17
Bilinear operations $\mathbb{L}_{\nu_{1},\nu_{2};\nu}$       3 39
Bilinear operations $\mathbb{L}_{\nu_{1},\nu_{2};\nu}$ , applied to Eisenstein distr.      69
Bilinear operations $\mathbb{L}_{\nu_{1},\nu_{2};\nu}$ , transferred to $\Pi$       71 73
Cohen products      1
Coherent states      121
Composition of homogeneous symbols      35 40
Composition of symbols      4 40 184 185
Continued fractions      215
Cusp forms      3 51 61
Dirac's comb      163
Dirichlet series with the $\lambda_{k}$ 's as poles      151 152
Distribution space $\mathcal{D}'_{y}$       14
Distribution space $\mathcal{D}'_{y}$ , modular distribution      17
Eisenstein series      5 19 61
Eisenstein series, distribution      17 19
Euler operator      26
Fourier coefficients and $L^{2}$ -norm      62
Fourier coefficients as hyperfunctions      56
Fourier coefficients of Eisenstein distrib.      21
Fourier coefficients of forms      20
Generating series of cusp-forms      153
Generating series of cusp-forms, their Fourier coefficients      156
Generating series of cusp-forms, their polar parts      157 160
Hecke operators      7 70 132 173
Holomorphic discrete series      177
homogeneous functions      28
Horocyclic calculus      182
Hyperbolic distance      25
Hyperfunctions      46 56 64
Infinitesimal operators      11
Intertwining operator      13 22 29
Iwasawa decomposition      25
Kloosterman sums      91

L-function      131 145
Lax — Phillips theory      194
Maass — Hecke forms      131
Mehler's formula      27
Metaplectic representation      119 179
Odd zeta series $\zeta_{n}$ in two variables      95 112
p-adic calculations      168
Petersson space $L^{2}(\Gamma \backslash \Pi)$       48
Poisson bracket      73
Poisson bracket of Eisenstein series      111
Product of Eisenstein series      78
Product of Eisenstein series, continuous part of product      89
Product of Eisenstein series, continuous part of red. prod.      84
Product of Eisenstein series, discrete part of red. prod.      101
Quadratic fields      216
Radon (dual) transform      25
Radon in an $L^{2}$ -context      27
Radon transform      4 25
Rankin — Selberg unfolding method      66
Recovering Fourier coefficients of forms      66
Reduced Poisson bracket of Eisenstein series      111
Reduced product of Eisenstein series      80 82
Residues (cuspidal)      19
Residues of zeta series $\zeta_{n}$ in two variables      141
Resolution of identity      121
Roelcke — Selberg expansion      5 50 61
Roelcke — Selberg expansion of Poisson bracket      145
Roelcke — Selberg expansion of product of Eisenstein series      89 133 138
Roelcke — Selberg expansion of reduced Poisson bracket      112
Roelcke — Selberg expansion of reduced product of Eisenstein series      84 101
Symbolic calculi      179
Symplectic Fourier transf.      26
Weber — Schafheitlin integral      46 72 88 105
Weyl calculus      33
Wigner function      121
Zeros of zeta function      97 101 108 151 152 157
Zeta series $\zeta_{n}$ in two variables      91 108
Zeta series $\zeta_{n}$ in two variables, link with Kloosterman sums      93

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