Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms

Unterberger, Andre

ISBN 10: 3034801653 / ISBN 13: 9783034801652

Editore: Birkhäuser, 2011

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Dati bibliografici

• Titolo: Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms
• Editore: Birkhäuser
• Data di pubblicazione: 2011
• Lingua: Inglese
• ISBN 10: 3034801653
• ISBN 13: 9783034801652
• Rilegatura: Brossura
• Condizione: New

Descrizione articolo

Riassunto

Pseudodifferential analysis, introduced in this book in a way adapted to the needs of number theorists, relates automorphic function theory in the hyperbolic half-plane Π to automorphic distribution theory in the plane. Spectral-theoretic questions are discussed in one or the other environment: in the latter one, the problem of decomposing automorphic functions in Π according to the spectral decomposition of the modular Laplacian gives way to the simpler one of decomposing automorphic distributions in R² into homogeneous components. The Poincaré summation process, which consists in building automorphic distributions as series of g-transforms, for g E SL(2;Z), of some initial function, say in S(R²), is analyzed in detail. On Π, a large class of new automorphic functions or measures is built in the same way: one of its features lies in an interpretation, as a spectral density, of the restriction of the zeta function to any line within the critical strip.

The book is addressed to a wide audience of advanced graduate students and researchers working in analytic number theory or pseudo-differential analysis.

Dalla quarta di copertina

Pseudodifferential analysis, introduced in this book in a way adapted to the needs of number theorists, relates automorphic function theory in the hyperbolic half-plane ? to automorphic distribution theory in the plane. Spectral-theoretic questions are discussed in one or the other environment: in the latter one, the problem of decomposing automorphic functions in ? according to the spectral decomposition of the modular Laplacian gives way to the simpler one of decomposing automorphic distributions in R² into homogeneous components. The Poincaré summation process, which consists in building automorphic distributions as series of g-transforms, for g Î SL(2;Z), of some initial function, say in S(R²), is analyzed in detail. On ?, a large class of new automorphic functions or measures is built in the same way: one of its features lies in an interpretation, as a spectral density, of the restriction of the zeta function to any line within the critical strip.

The book is addressed to a wide audience of advanced graduate students and researchers working in analytic number theory or pseudo-differential analysis.