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Spectral means of central values of automorphic L-functions for GL(2) / Masao Tsuzuki.

By: Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v 235, no 1110.Publication details: Providence : American Mathematical Society, 2015.Description: vii, 129 p. ; 26 cmISBN:
  • 9781470410193 (pbk. : alk. paper)
Subject(s): DDC classification:
  • 510 23 Am512
Contents:
1. Introduction -- 2. Preliminaries -- 3. Preliminary analysis -- 4. Green's functions on GL(2, [real numbers]) -- 5. Green's functions on GL(2,Fv) with v a non archimedian 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 -- Bibliography.
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.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 510 Am512 (Browse shelf(Opens below)) Available 136681
Total holds: 0

Includes bibliographical references.

1. Introduction --
2. Preliminaries --
3. Preliminary analysis --
4. Green's functions on GL(2, [real numbers]) --
5. Green's functions on GL(2,Fv) with v a non archimedian 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 --
Bibliography.

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.

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