Student Seminar: Number Theory and Automorphic Forms

Organizers: Lior Silberman, Julia Gordon, Bill Casselman.

Contact: lior @ math.ubc.ca MATX 1112 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.

Agenda

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  

References

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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