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Spectral Means of Central Values of Automorphic

By: Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence, RI : American Mathematical Society, 2015Copyright date: ©2015Edition: 1st edDescription: 1 online resource (144 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470422288
Subject(s): Genre/Form: Additional physical formats: Print version:: Spectral Means of Central Values of Automorphic DDC classification:
  • 515/.9
LOC classification:
  • QA353.A9 -- .T789 2014eb
Online resources:
Contents:
Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Preliminaries -- Chapter 3. Preliminary analysis -- Chapter 4. Green's functions on (2,ℝ) -- Chapter 5. Green's functions on (2, ᵥ) with a non archimedean place -- Chapter 6. Kernel functions -- Chapter 7. Regularized periods -- Chapter 8. Automorphic Green's functions -- Chapter 9. Automorphic smoothed kernels -- Chapter 10. Periods of regularized automorphic smoothed kernels: the spectral side -- Chapter 11. A geometric expression of automorphic smoothed kernels -- Chapter 12. Periods of regularized automorphic smoothed kernels: the geometric side -- Chapter 13. Asymptotic formulas -- Chapter 14. An error term estimate in the Weyl type asymptotic law -- Chapter 15. Appendix -- Bibliography -- Back Cover.
Summary: Starting with Green's functions on adele points of \mathrm{GL}(2) considered over a totally real number field, the author elaborates an explicit version of the relative trace formula, whose spectral side encodes the informaton on period integrals of cuspidal waveforms along a maximal split torus. As an application, he proves two kinds of asymptotic mean formula for certain central L-values attached to cuspidal waveforms with square-free level.
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Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Preliminaries -- Chapter 3. Preliminary analysis -- Chapter 4. Green's functions on (2,ℝ) -- Chapter 5. Green's functions on (2, ᵥ) with a non archimedean place -- Chapter 6. Kernel functions -- Chapter 7. Regularized periods -- Chapter 8. Automorphic Green's functions -- Chapter 9. Automorphic smoothed kernels -- Chapter 10. Periods of regularized automorphic smoothed kernels: the spectral side -- Chapter 11. A geometric expression of automorphic smoothed kernels -- Chapter 12. Periods of regularized automorphic smoothed kernels: the geometric side -- Chapter 13. Asymptotic formulas -- Chapter 14. An error term estimate in the Weyl type asymptotic law -- Chapter 15. Appendix -- Bibliography -- Back Cover.

Starting with Green's functions on adele points of \mathrm{GL}(2) considered over a totally real number field, the author elaborates an explicit version of the relative trace formula, whose spectral side encodes the informaton on period integrals of cuspidal waveforms along a maximal split torus. As an application, he proves two kinds of asymptotic mean formula for certain central L-values attached to cuspidal waveforms with square-free level.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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