Student Seminar: Number Theory and Automorphic Forms

Organizers: Lior Silberman, Bill Casselman, Julia Gordon.

Contact: lior @ math.ubc.ca ; MATH 229B ; 604-827-3031

Fall 2008: Real-Analytic forms and Eisenstein Series


Agenda

Meeting Title Speaker Notes & References
1. (2/9) Holomorphic forms Lior Silberman [7]
2. (11/9) Hilbert spaces and self-adjoint operators Bill Casselman [6]
3. (18/9) Hyperbolic geometry Hesam Abbaspour
4. (25/9) Hyperbolic geometry
Maass forms
Lior Silberman
Scott Sitar
notes
[3]
5. (2/10) Absolute convergence of Eisenstein series Alia Hamieh [5]
6. (7/10) Compact operators and the resolvent
Analytical continuation of Eisenstein series
Lior Silberman
Jay Heumann
[2]
[4]
7. (16/10) The analytical continuation (ctd)
Representation Theory of SL_2(R)
Jay Heumann
Julia Gordon
8. (23/10) Representation Theory of SL_2(R), continued Julia Gordon
9. (6/11) Maass forms associated to real quadratic fields
L-functions associated to Maass forms
Hesam Abbaspour
10. (13/11) Hecke operators the Euler product Scott Sitar [1]
11. (20/11) Adeles and adelic groups Jay Heumann
12. (27/11) The adelic perspective Alia Hamieh [1]

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] 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
[4] Continuation of E. Series Jacquet Note on the analytic continuation of Eisenstein series Proc. Sympos. Pure Math. 61 (1997), 407–412. MR: 1476506
[5] Convergence of E. series Kubota Elementary theory of Eisenstein series Halsten Press, New York, 1973. xi+110 pp. MR: 0429749
[6] 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
[7] 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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