Quantization and Non-holomorphic Modular Forms

André Unterberger (Autor)

Buch | Softcover

X, 258 Seiten

2000 | 2000
Springer Berlin (Verlag)
978-3-540-67861-8 (ISBN)

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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).

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.

Erscheint lt. Verlag	28.8.2000
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	X, 258 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	381 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	11F03 • 11L05 • 35S99 • 44A12 • 81S99 • automorphic distributions • Boundary value problem • Hardcover, Softcover / Mathematik/Arithmetik, Algebra • HC/Mathematik/Arithmetik, Algebra • Kloosterman series • Lax-Phillips theory • Modulform • Non-holomorphic modular forms • Quantisierung • Rankin-Cohen products • scattering theory • wave equation
ISBN-10	3-540-67861-1 / 3540678611
ISBN-13	978-3-540-67861-8 / 9783540678618
Zustand	Neuware