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Spectral Means of Central Values of Automorphic $L$-Functions for GL(2)
 
Masao Tsuzuki :  Sophia University, Tokyo, Japan
Spectral Means of Central Values of Automorphic $L$-Functions for GL(2)
eBook ISBN:  978-1-4704-2228-8
Product Code:  MEMO/235/1110.E
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
Add to cart
Spectral Means of Central Values of Automorphic $L$-Functions for GL(2)
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Spectral Means of Central Values of Automorphic $L$-Functions for GL(2)
Masao Tsuzuki :  Sophia University, Tokyo, Japan
eBook ISBN:  978-1-4704-2228-8
Product Code:  MEMO/235/1110.E
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
Add to cart
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 235; 2015; 129 pp
    MSC: Primary 11

    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.
  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Preliminaries
    • 3. Preliminary analysis
    • 4. Green’s functions on $\mathrm {GL}(2,\mathbb {R})$
    • 5. Green’s functions on $\mathrm {GL}(2,F_v)$ with $v$ a non archimedean place
    • 6. Kernel functions
    • 7. Regularized periods
    • 8. Automorphic Green’s functions
    • 9. Automorphic smoothed kernels
    • 10. Periods of regularized automorphic smoothed kernels: the spectral side
    • 11. A geometric expression of automorphic smoothed kernels
    • 12. Periods of regularized automorphic smoothed kernels: the geometric side
    • 13. Asymptotic formulas
    • 14. An error term estimate in the Weyl type asymptotic law
    • 15. Appendix
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Memoirs of the American Mathematical Society
Volume: 235; 2015; 129 pp
MSC: Primary 11

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.
  • Chapters
  • 1. Introduction
  • 2. Preliminaries
  • 3. Preliminary analysis
  • 4. Green’s functions on $\mathrm {GL}(2,\mathbb {R})$
  • 5. Green’s functions on $\mathrm {GL}(2,F_v)$ with $v$ a non archimedean place
  • 6. Kernel functions
  • 7. Regularized periods
  • 8. Automorphic Green’s functions
  • 9. Automorphic smoothed kernels
  • 10. Periods of regularized automorphic smoothed kernels: the spectral side
  • 11. A geometric expression of automorphic smoothed kernels
  • 12. Periods of regularized automorphic smoothed kernels: the geometric side
  • 13. Asymptotic formulas
  • 14. An error term estimate in the Weyl type asymptotic law
  • 15. Appendix
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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