Student Seminar: Number Theory and Automorphic Forms

Organizers: Lior Silberman, Julia Gordon, Bill Casselman.

Contact: lior @ MATH 229B 604-827-3031

Fall 2014: Continuation of Eisenstein Series

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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