Organizers: Lior Silberman, Julia Gordon, Bill Casselman.
Contact: lior | @ | math.ubc.ca | MATH 229B | 604-827-3031 |
We will analytically continue the non-holomorphic Eisenstein series on the modular surface. This will both be an introduction to automorphic forms and to spectral theory. Very little background will be assumed.
Meeting | Title | Speaker | Notes & References |
---|---|---|---|
1. 11/9 | Introduction | Lior Silberman | |
2. 18/9 | Hyperbolic geometry | Reza Sadoughi | |
3. 25/9 | Maass forms, Fourier Expansion | Subhajit Jana | [4] |
4. 2/10 | Absolute convergence of Eisenstein series | Ed Belk | [6] |
5. 9/10 | Spectral Theory: Sobolev embedding, compact operators, self-adjoint operators and the Laplacian |
Lior Silberman | [7] |
6. 23/10 | Analytical continuation of Eisenstein series I | Qiang Zhang | [2], [3] |
7. 30/10 | Analytical continuation of Eisenstein series II | Athena Nguyen | [2], [3] |
8. 6/11 | The spectral decomposition | Lior Silberman | [4] |
9. 13/11 | Rankin–Selberg | Adela Gherga | [4] |
10. 20/11 | p-adic analgoues | David Roe |
Topics | Author(s) | Title | Data | |
---|---|---|---|---|
[1] | Bump | Automorphic forms and representations | CSM No. 53. Cambridge University Press, Cambridge, 1997. xiv+574 pp. ISBN: 0-521-55098-X, MR: 1431508 | |
[2] | Continuation of E. Series | Colin de Verdière | Une nouvelle démonstration du prolongement méromorphe des séries d'Eisenstein | C. R. Acad. Sci. Paris Sér. I Math. 293 (1981), no. 7, 361–363. MR: 0639175 |
[3] | Continuation of E. Series | Garrett | Colin de Verdière's meromorphic continuation of Eisenstein series | online |
[4] | Maass forms, the space Γ\H | Iwaniec | Spectral Methods of Automorphic Forms | 2nd edition. GSM No. 53. AMS, Providence, RI, 2002. xii+220 pp. ISBN: 0-8218-3160-7, MR: 1942691 |
[5] | Continuation of E. Series | Jacquet | Note on the analytic continuation of Eisenstein series | Proc. Sympos. Pure Math. 61 (1997), 407–412. MR: 1476506 |
[6] | Convergence of E. series | Kubota | Elementary theory of Eisenstein series | Halsten Press, New York, 1973. xi+110 pp. MR: 0429749 |
[7] | Hilbert spaces, Elliptic Regularity, Fourier Analysis | Reed and Simon | Methods of modern mathematical physics I: Functional analysis | 2nd edition. Academic Press, New York, 1980. xv+400 pp. ISBN: 0-12-585050-6, MR: 0751959 |
[8] | Quadratic forms and modular forms | Serre | A Course in Arithmetic | GTM No. 7. Springer-Verlag, New York-Heidelberg, 1973. viii+115 pp. ISBN: 0-38-7900403-0, MR: 0255476 |
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Last modified Tuesday January 20, 2015