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Course by O. G. Balkanova "Spectral theory and the Kuznetsov trace formula"
(September 16–December 23, 2020, online via Zoom, Moscow)
The purpose of this course is to learn some basic spectral methods that
are used to solve a wide range of problems in analytic number theory.
One of the most significant results in this direction is the Kuznetsov
trace formula, which establishes the relationship between Kloosterman
sums and the sums of the Fourier coefficients of Hecke–Maass forms and
Eisenstein series. We will study a detailed proof of the Kuznetsov
formula and its various applications. The program includes the following
topics:
- Classical modular forms
- Poincaré and Eisenstein series
- Kloosterman sums
- Petersson trace formula
- Kuznetsov trace formula
- L-functions
Financial support. The course is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no. 075-15-2019-1614).
 Program
Lecturer
Balkanova Olga Germanovna
Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center |
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| Course by O. G. Balkanova "Spectral theory and the Kuznetsov trace formula", Moscow, September 16–December 23, 2020 |
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December 23, 2020 (Wed) |
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Lecture 15. Spectral theory and the Kuznetsov trace formula
O. G. Balkanova
December 23, 2020 18:00, Moscow, online via Zoom
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December 16, 2020 (Wed) |
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Lecture 14. Spectral theory and the Kuznetsov trace formula
O. G. Balkanova
December 16, 2020 18:00, Moscow, online via Zoom
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December 9, 2020 (Wed) |
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Lecture 13. Spectral theory and the Kuznetsov trace formula
O. G. Balkanova
December 9, 2020 18:00, Moscow, online via Zoom
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December 2, 2020 (Wed) |
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Lecture 12. Spectral theory and the Kuznetsov trace formula
O. G. Balkanova
December 2, 2020 18:00, Moscow, online via Zoom
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November 25, 2020 (Wed) |
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Lecture 11. Spectral theory and the Kuznetsov trace formula
O. G. Balkanova
November 25, 2020 18:00, Moscow, online via Zoom
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November 18, 2020 (Wed) |
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Lecture 10. Spectral theory and the Kuznetsov trace formula
O. G. Balkanova
November 18, 2020 18:00, Moscow, online via Zoom
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November 11, 2020 (Wed) |
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Lecture 9. Spectral theory and the Kuznetsov trace formula
O. G. Balkanova
November 11, 2020 18:00, Moscow, online via Zoom
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November 4, 2020 (Wed) |
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Lecture 8. Spectral theory and the Kuznetsov trace formula
O. G. Balkanova
November 4, 2020 18:00, Moscow, online via Zoom
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October 28, 2020 (Wed) |
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Lecture 7. Spectral theory and the Kuznetsov trace formula
O. G. Balkanova
October 28, 2020 18:00, Moscow, online via Zoom
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October 21, 2020 (Wed) |
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Lecture 6. Spectral theory and the Kuznetsov trace formula
O. G. Balkanova
October 21, 2020 18:00, Moscow, online via Zoom
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October 14, 2020 (Wed) |
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Lecture 5. Spectral theory and the Kuznetsov trace formula
O. G. Balkanova
October 14, 2020 18:00, Moscow, online via Zoom
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October 7, 2020 (Wed) |
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Lecture 4. Spectral theory and the Kuznetsov trace formula
O. G. Balkanova
October 7, 2020 18:00, Moscow, online via Zoom
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September 30, 2020 (Wed) |
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Lecture 3. Spectral theory and the Kuznetsov trace formula
O. G. Balkanova
September 30, 2020 18:00, Moscow, online via Zoom
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September 23, 2020 (Wed) |
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Lecture 2. Spectral theory and the Kuznetsov trace formula
O. G. Balkanova
September 23, 2020 18:00, Moscow, online via Zoom
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September 16, 2020 (Wed) |
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Lecture 1. Spectral theory and the Kuznetsov trace formula
O. G. Balkanova
September 16, 2020 18:00, Moscow, online via Zoom
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