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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms

Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms

Unterberger, André

Paperback

Series: Pseudo-Differential Operators, Book 8

General Mathematics

ISBN10: 3034801653
ISBN13: 9783034801652
Publisher: Birkhauser
Published: Aug 6 2011
Pages: 300
Weight: 1.05
Height: 0.70 Width: 6.60 Depth: 9.50
Language: English

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.

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