Quantization and Non-holomorphic Modular Forms

• Main Author: Unterberger, André (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2000.
• Edition: 1st ed. 2000.
• Series: Lecture Notes in Mathematics, 1742
• Subjects: Number theory.; Number Theory.

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 le...

Table of Contents:

• 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.